Hey Jil
No, I am afraid you don't have the right to ask people to stay sober with you. But you do have a choice over what you do and where you go. Don't go places where you feel that uncomfortable. Have you made any efforts to meet new friends who maybe don't drink so much, or at least some people who you socialise with doing non drinking activities. I have been lucky enough to meet a few people in sobriety who I don't even know if they drink or not as we have never been in a situation where that would come up. That is pretty miraculous to me when I compare it to my old life.
I also think recovery is something you have to maintain. It doesn't have to be AA but if you are doing nothing for your recovery then it is not surprising you feel the way you do. The best thing I can suggest is to get out of your own head and help someone else. Try and help some of those newbies who are struggling to string a few days together, volunteer somewhere, which is a great way to meet people too. But also I think it's necessary to do something about those thoughts you have too. Maybe something like alen carr's book or jason vale's. There is a lot of recovery stuff out there which is not AA. But even the AA literature is really good. Get reading and try and find what will work for you. Or maybe some CBT to help you change your thought patterns. Oh, and definitely post here more