I am surprised you even started your course without having dealt with the issue first. These situations were bound to crop up and will do so in years 2 and 3.
It sounds rubbish to sit on your own.
Ok my advice is and its counter intuitive. You do have to contact your lecturer and point out you have an issue. they should know about it. They might find it acceptable if you sort something out with your group.
1. Contact each of the group via e-mail or snapchat and explain how it affects you, that you are receiving medical treatment and the group work poses a problem.You realise it is your issue and not theirs. You still want to contribute and play your part, so you have come up with some ideas..
2. Group video. Not everyone needs to be on camera. perhaps you can contribute doing some other tasks like production,editing or sound?
3. Group meetings and ideas. Perhpas you cnat manage in person, but maybe a message board forum can be set up and you can contribute ideas on there or a snapchat group. Wuld any of them have problems with that?
4. Similar with the group essay. You could submit ideas in writing or via messenger. Its nothing personal but a group meeting is too much for you. maybe you cna skype or they can skype and you can listen and type.
5. When it comes to writing, then you could eb in charge of a particular section, plus proof reading ect. Stuff you can do on your own.
Its a shame you dont have a friend who could act as go between for you. Any reasonable students would be happy to make some allowances imo as long as you pulled your weight. Doing the above could work as a stop gap.
How much counseling/ therapy are you getting? Do they know about your issues?
If you arent in contact then get in touch with your diasbility/ student support team. You need to let your tutor and the lecturer know. Perhaps they can find a way to work round it? At some stage you have to take some measure to deal with it as in the real world you will be expected to talk to people and work in groups.
https://www.anxietyuk.org.uk/our-services/get-help/http://www.mind.org.uk/information-support/your-stories/confronting-my-social-anxiety-at-university/http://www.nopanic.org.uk/ Youth Helpline 0330 606 1174 (For 13 to 20 year olds, open 3pm to 6pm Monday to Friday, Landline rates apply)