I used to have a very similar reaction to panic attacks when I first started getting them.
It didn't matter what anyone else said to me to try and convince me that I was OK....I thought I was going to have a heart attack. Even after I went to a cardiologist and had an EKG (that ruled out a heart problem), I still was not convinced.
Until I started seeing a psychologist.......This is how she helped me get over my fear. During a session, she helped me bring on a panic attack, and then had me get up and start doing jumping jacks (yes...Jumping Jacks!), until I got over the worst part of the attack....She explained that " if I was really having a heart attack, it would be impossible for me to do the jumping jacks".
So now I had physical proof that I was not going to die from the panic attacks....From then on, each time I started to have an attack, I did some form of exercise to prove to myself that I was OK.
This technique helped me so much, and I hope that it may bring you some comfort, if you choose to try it.