Hi,
It is important to consult your physician regarding this question as he/she knows exactly your condition and other medications your are taking.
In general, birth control pills should be OK to take concurrently with a heart condition. You can explore other methods of birth control to ease your fears such as IUDs and the NuvaRing. IUDs are inserted into the uterus through the vagina and prevent implantation of pregancy. The ring is placed in the vagina next to the cervix and locally releases hormones to prevent pregancy. It remains in place for 3 weeks.
Hope this helps,
-HealthSupport