I'd talk to the doctor that prescribed them. Are they for thyroid issues?
I think they are studying things more and more. I have not seen those medications listed as either drugs or conditions that there is an issue with the vaccine. They may judge risk vs. benefit for complicated patient histories. I hope you can get it!
There's no risk getting the vaccine with, either hypothyroidism or Levothyroxine. I have Hashimoto's and take Levoxyl (brand of Levo). I'm fully vaccinated (both shots) and have had no trouble. I know several other people who are also hypo who have been vaccinated, plus I've also read several articles that indicate there's no problem getting the vaccine with Hashimoto's.
As for the Hydroxychloroquine and high ESR - my concern would be what's causing the high ESR. Hydroxychloroquine is, typically, used to treat things like Lupus and Rheumatoid Arthritis. Both of those would indicate compromised immune system, which would call for getting the vaccine asap. My daughter has Lupus and her doctor wanted her to get the shot asap since the virus would be harder on her than the vaccine. She used to be on Hydroxychloroquine, but I'm not sure if she still is.
To be on the safe side, I'd go ahead and make the appointment for the vaccine, but check with my doctor to be certain, in the meantime. You can always cancel the appointment if your doctor says not to get vaccinated,