So are you pregnant or not pregnant?

On your general predicament: I think that when you say that you are not a cheater, you are trying to say that you reported the incident to your boyfriend immediately, do not plan to have sex with the man again, did not have an intent to have sex with that man, so the elements of calculated, cold, premeditated, planned sex outside of your new relationship are missing, plus, repeatability is, we hope, no present as well. This is all valid, plus, "cheating" as a word means gaming the system - consider academic cheating, cheating on the income tax return, etc.

cheat
CHēt/
verb
1.
act dishonestly or unfairly in order to gain an advantage, esp. in a game or examination.
"she always cheats at cards"
swindle, defraud, deceive, trick, scam, dupe, hoodwink, double-cross, gull; More
informal
be sexually unfaithful.
"his wife was cheating on him"
synonyms: commit adultery, be unfaithful, stray; More
2.
avoid (something undesirable) by luck or skill.
"she cheated death in a spectacular crash"
synonyms: avoid, escape, evade, elude; More
archaic
help (time) pass.
"the tuneless rhyme with which the warder cheats the time"
noun
noun: cheat; plural noun: cheats
1.
a person who behaves dishonestly in order to gain an advantage.
"a liar and a cheat"
synonyms: swindler, cheater, fraudster, trickster, deceiver, hoaxer, double-dealer, double-crosser, sham, fraud, fake, charlatan, quack, crook, snake oil salesman, mountebank; More

So the operative words are deceit and taking advantage, and I do not see you as doing any of that - you rather seem to be a lost and hapless creature. So I think (see emphasis above) that you strayed - it is listed as a synonym of cheating, but it is not a full synonym, because the connotations are so different. You cannot stray on your income tax return, etc. So - you strayed as a result of a lapse of judgment provoked by alcohol.

Expressing the feelings of guilt and remorse towards the boyfriend would be appropriate if you do not overdo it - remember that he lost his kids to the ex spouse, and as somebody who has been through that, I can tell you that he is, most likely, constantly thinking of his kids and grieving the way of life he had when his kids lived with you. So you need to be supportive of him in that grieving, and if you keep saying that you were horribly guilty again and again, you would make it all about you (it would be a twisted form of attention seeking). So sort of say it, but also try your best to figure out what he currently needs in terms of emotional support. Is he getting visitation with the kids? Do you know the kids? If you know him, will you be present during visitation? If you will be present, then it is important that you be prepared - have some games to play with them, cook for them, etc. If you want to become a permanent fixture in his life, learning to interact positively with his kid would be key. In general, what I am trying to say that you are currently consumed by guilt, worry, fear of his resentment, and are as a result self-centered, which is not helping your relationship given his divorce crisis. Of course, if HE told you that the major fear he has left as an aftertaste of the divorce is the fear that you might leave him, then, perhaps, it is his major current concern, but unless he expressly and explicitly told you so, expect him to be in emotional pain on account of losing his children. IT IS NOT ALL ABOUT YOU in his life.

After you have expressed your feelings of guilt and remorse, you need to come up with a plan of prevention. In other words, you need to THINK.

Intelligent people start with recognizing patterns - a good portion of IQ testing is pattern recognition, and even autistic, non-verbal children are able to recognize visual patterns.

So you noticed what your pattern is, and that was intelligent of you. Your pattern is ALCOHOL in a SOCIAL setting --> DEMONS resurfacing, or, alternatively, MONSTERS -->lapses of judgment that result in sex you later regret having.

OK, so now we have two approaches. The simple approach is not to drink alcohol when your boyfriend is not around. It guarantees results, because your demons resurface only when you drink. Alcohol in moderation is a wonderful thing that aids social cohesion and offers numerous health benefits, so I am not saying that you should give up alcohol - drink it at home with your boyfriend, or in social settings when your boyfriend is by your side, but not when you are alone at parties.

This approach is difficult because it is hard to reject offers of alcohol at parties - you will have to be disciplined. My migraine attacks, it turned out, were triggered by coffee, so I now do not drink coffee but rather drink tea. When I get invited for a chat over coffee, I order tea or hot chocolate, saying that coffee triggers horrible headaches in me. Alcohol can trigger migraines, but luckily does not for me, but I am offering it for you as an easy way out - 9 Common Migraine Triggers

Since this is a mental health site, I imagine that you might have mental illness and might be on medications that interact with alcohol, but you do not want to say "I do not drink alcohol because of my psych medications", and blaming a migraine attack would not give away your mental health issues.

Another thing - do you know about the basic hygiene of alcohol consumption? In other words, do you know to eat a complete meal with alcohol, and, to have 1:1 one full non-alcoholic drink per each alcoholic drink? If you have not been doing that, then maybe you can experiment with the proper drinking routine, because well fed and well hydrated, your brain will be much better able to make the right judgment without lapses.

The second approach is to try therapy to deal with the underlying causes of demons and monsters, but that would take a very long time, so even if you plan on doing that, not drinking socially while your boyfriend is away is still the right stopgap measure to take.

Finally, once you decide what to do, and you need to formulate a plan of preventing further incidents of lapses of judgment, present it to your boyfriend, orally or in writing. He will be impressed that you have applied problem solving skills to nip the issue in the bud. It would much more impressive than repeated declarations of remorse, because it would show that you really care about not straying in the future. Say, I am probably twice your age, so let us assume that we are inside a company and I am your boss and you are my report. And, you did something awful. Just completely awful. And, there is a good chance that you will do it again. So let us say we have a one-on-one meeting, and during which you cry and sob and repeat that what you did was the most horrible thing on Earth. And, you cry and sob and cry and sob and repeat that you feel guilty. Initially, I would let you cry and sob, realizing that you are in a tough place emotionally, but eventually I will start looking at my watch hoping that you would realize that you are wasting my time, and get your act together. Once you are done sobbing, I already have another meeting to go to, so we postpone discussing the incident until later. I have a lot of stuff going on, with tight deadlines, and I postpone discussing a plan on how you would not make the same horrible mistake in the future. I go about my business and soon learn that you made that same mistake again. I call you to my office and you sob even more, explaining that your guilt was so overpowering that you completely lost your bearings and did not notice how you made the same mistake again. I fire you.

Cf. you come to my office after the first incident and say: "I am really sorry for the pain I caused you. I understand that I lost all credibility with you, but I hope to regain your trust via stellar performance in the future. I have done a post mortem (root cause analysis) on the incident, discovered why what went wrong went wrong, and developed a plan that solves the problem that caused the incident upstream (in your case, getting rid of the demons in therapy and/or abstaining from alcohol when not in your bf's presence are ways to solve the problem upstream, as opposed to continuing on as usual, consuming alcohol, and relying on willpower, which would be an attempt to solve the problem downstream, when it is usually much harder to solve it). Here is my plan to review."

I look at the plan and it strikes me as a well thought out plan. I give you a couple of suggestions for minor changes but otherwise acknowledge that I am glad that you have devised a good plan and that I will be available for further feedback and support in the process of your implementing your plan. I leave the office glad that you seem to be on the right track, and eventually, not seeing any more incidents, I regain trust in your professionalism.

See the difference? It was a bit of the art of project management applied to drunken straying girlfriends