When you mentioned birth control pills, it reminded me that the risk of blood clots increased for women who were smokers. Not sure if that applies here with the vax as well. Anyway, we are not getting all of the info that medical experts are yet.
I happened to be on the pill for most of my entire reproductive life, a non smoker, and no issues at all. Got the J&J, and other than extreme fatigue and aches for 24 hours, was fine after.
I’m glad for all of the industry’s caution, but I’d say — try not to be worried, and I hope you can get this vax or whatever is available as soon as possible.