Often matching the "right" anti-depressant (a SSRI like Prozac, an SNRI or any of the others) to the "right" person is a matter of trial and error.

As far as I can see heart issues are possible but rare side-effects of Prozac (Prozac Uses, Dosage, Side Effects & Warnings - Drugs.com).

If you find that Prozac is not helping you or if you have heart problems because of it then discussing other possibilities with your doctor is an option.