It sounds like there are people that genuinely care about you. I don’t think they would keep in touch if they did not. 
I can understand that the same people may have expressed how your anxiety and/ or depression affects your friendship/ relationship. But hey, who DOENS’T suffer from some form or level of anxiety or depression these days? Being open and honest about your struggles isn’t easy, but you’re doing it, and you should give yourself some credit for that.
If you feel like you want to make mends and salvage these relationships, I think it is very possible. However, my advise would be to do that by taking time to work on yourself first. I cannot emphasize how important of a role therapy has played in helping me and others through anxiety and depression. It’s an ongoing lifelong process, but it will be, in my opinion, the most constructive thing you can do. 
Working on yourself and learning more about yourself will ultimately build your confidence and ability to connect with others, and you’ll know when you’re ready to start reaching out. Moreover, I think your friends will recognize the effort you are putting in by going to therapy, and that in itself will show them that you care enough to make positive changes for your sake and for those relationships you care about.
Good luck!