The 'pull out' method isn't the most reliable in the world so yeah, you could be pregnant. But, that's impossible to know until you either give birth or take a pregnancy test
Do one ASAP, but if its negative do another one at a later date, say a few days maybe a week after the first one. If you don't see your period by the time you reach the longest time you'd have to wait, then test again. Very occasionally some women will keep getting negative results with a urine test, so if you're still worried after doing the above, or your period still doesn't show, then ask your doctor for a blood test and explain what's going on.
If you're not pregnant and you don't want to become pregnant then I'd seriously look at other methods of contraception because unless you know your cycle inside out, which you don't, then your current method really isn't a safe one and even if you did know your cycle like the back of your hand, I'd not like to rely on that anyway. The implant can be great because its there for three years and means you don't have to remember taking anything, but you have to be careful if you have any mental health problems because it can trigger depression. I had it with no adverse effects, I didn't even get a period while using it which was great! But it's not for everyone. I'm sure your doctor will be happy to talk through other means though if that's not for you. Having said that about pulling out, I did the same myself many years ago and never got pregnant. So it doesn't by any means mean that you definitely are, it's just not reliable enough at all if you really don't want to be.
Anyway, I hope you get the outcome you want, and I hope you're ok.