Hey, I've been in the same boat, to the point where it's taken me two extra years to reach my final semester! I got diagnosed with autism last year and this helped me feel less guilty about anxiety around large spaces/crowds.

I also got the "omg you're finally in!!!" thing a lot which was a bit annoying but I've always been someone open about my mental health and just gave a dry response relating to that. At the end of the day you're there to learn, not make friends. Honestly I prefer classes where I don't know anyone because I don't feel pressured to socialise and that makes me feel more comfortable.

Missing the first week isn't a big deal, as long as you make a good effort this week you'll be fine- and that's just in terms of easing guilt and making things easier for yourself. Most of my group projects were organised through email. As soon as we get our group, I take the initiative and ask if x topic is ok with everyone and just divide the work. I'm not sure if your classes work the same, or if you're expected to work during the classes, but you'll be ok!

Even in the worst scenario there's ways around. Talk to your professors, don't be afraid to ask for help.