Worried about birth control...

So I had my first visit to the OB-GYN this past Friday to have some tests run because I’ve been having abdominal pains and my period has gotten really irregular. She found a few small cysts on my right ovary but said they weren’t anything to be really concerned about right now, but to be safe, prescribed me a low-dose birth control to help with my abdominal pains, regulate my period, and lessen the development of any more cysts. *But* I’m a little worried about being on the pill because of my family history...My mom had a stroke after she was put on the pill when she was younger, and her aunt had issues related to the pill as well. Should I be concerned about this? Is there a chance that I won’t experience any negative side effects at all?