Is it possible for a woman to have a heart attack, then later get pregnant and have a healthy baby?

Yes: But it's exceptionally uncommon for a premenopausal woman to have heart attack unless she has diabetes, smokes, uses Cocaine or has a rare disease. That said, if health is otherwise good and heart disease has been treated and is stable, it is generally possible to successfully carry a child to term. I can't comment on the specifics for you though. Be evaluated.

Why not?: As long as you didn't have any serious damage to your heart muscle, don't have any residual untreated blockages and are otherwise healthy overall, should be possible. Please check with your cardiologist before you consider stopping birth control and actively pursue pregnancy.