These are good questions and my heart goes out to you since I’m sure this has been difficult for you.
I am speaking generally here because I can’t see you and these are general suggestions. Botox cannot cause myasthenia gravis but if you had it already (very mildly) and didn’t know it, it could make an existing case worse. I can’t tell from above if you’ve seen a neurologist (a specialist in nerve problems). Please see a neurologist if you haven’t already. This is too complicated a problem for most primary care doctors to handle.
Also, it is possible that you have something called a Bell’s palsy (very different than myasthenia gravis). Bell’s palsy can cause a one-sided facial droop. I had one patient years ago who developed Bell’s palsy close to a Botox injection. It resolved completely and she has had subsequent Botox with no problem. They were related in time but not causally. Again, a good neurologist will be able to give you the best diagnosis and treatment plan for this problem. Good luck!