You really seem to understand yourself and where you are right now and where you'd like to be, which is great. Sensory issues, learning problems and eye contact are not always attributable to AS and Asperger's, but they certainly can be,as you mentioned.
I think it is a good idea to get that evaluation whenever you can afford it or perhaps try to connect with people at a local University Psych department and see if they offer an free services or clinical trials that you might be interested and feel might benefit you, soo.
I do love research about this stuff and part of me when I read almost anything can see a little bit of myself in almost every diagnosis I read eventually, if I look hard enough. But I just focus on the main 2 challenges that i KNOW affect my life the most: MY ADHD and Dyslexia. I have meds and plans in place to work on those on an ongoing basis.

It's okay to be angry and frustrated, but overall, your tone is pretty positive, too, which is AWESOME! I think if you can even meet with someone to help you identify two main areas (ie. diagnoses and/or challenges) that you would like to work on (say for the next 6 months or a year) and create a plan (that may or may not include certain meds and strategies etc.), then you will make really good progress.

In my opinion, it seems like you might want to focus on: 1. developing meaningful and safe friendships with others (that could eventually lead to intimacy in the future) 2. Developing skills and strategies to not only pass your University entrance exam, but also to be successful at University (and you WILL need others' help to do so and please NEVER feel bad about that, many people do!!!) 3. Processing some of the abuse and neglect you suffered in your child to help you learn to "release" the hold this has on you in your adulthood (to the best of your ability) 4. Develop some strategies and coping skills for managing compulsions, emotions and frustrations etc. more appropriately and 5. Finding some passions and interests to explore and develop (and possibly to pursue at University) so you can develop some skills and abilities to find employment in the future.

I am sure there are many more things you'd like to work on and address, but perhaps these might be some of the ones you could choose to focus on and work through over the next several years??? These are big goals and you need time and support to work on them (and, again, please don't feel bad about that, we ALL have stuff we need to work on).

I think if you can connect with a therapist and/or agency to help get you started, you seem bright and aware enough to develop and implement (and even tweak and revise) plans to work on these things…One area and one step at a time.

It's a day by day thing and you are on the right track. You have MANY things going for you. Keep reaching out and keep moving forward to actively engage in your journey. Maybe keep a journal or notebook of your progress. If you choose an area to target, make a plan and then meet that goal and move on to the next…over time you will see great results (even if they seem like SMALL great results).

You can do this! Best of luck to you!