I'm sorry to say but I don't think one more person's opinion expert or otherwise will convince you it's not your heart. I sympathize that you're going through such a difficult time right now. Hormones can certainly flare anxiety, that was a big trigger for me in the post-partum period with my daughter. Also, now that you have this new little one depending on you, this may be causing thoughts about wanting to make sure you will be there for her for a long time and there's fear of the unknown that we can never guarantee it.
My advice: make sure there is someone to help support you with your little one, I know good sleep is near impossible with an infant but if possible be sure baby's father or another support person is helping with the evening care for you to rest, and in the day to when you can. Get out and get walking, it can be fun for you and the baby to enjoy nature together and exercise is important for recovery for anxiety and the postpartum period. make sure you're eating regularly, and consuming regular protein and water.
Look online for health anxiety workbooks. I'm a big proponent of these kind of things, and certainly see your doctor and get their advice on treatment, be it therapy medication, meditation, or whatever else the two of you feel is appropriate.
Best of luck and congratulations on your new baby!