The severe spasms I had in 04 did many of the same things to me.

I could feel my heart thumping in my chest, but it was beating steady & regularly. I was considering going to the hospital for awhile.
But I was pretty sure it was related to the extreme over use a couple days earlier.
If it was a heart attack I think it would have hit me during the extreme/overuse activity- that was just my logic and my risk.
I wasn't on any meds or didn't have any other complicating conditions.

I did feel like I had to cough a lot - because of the chest muscle spasms
There was inner vibrating - or it felt like that anyway..it was making me have to cough.

My upper back, neck & chest muscles were locked up very tight.

The very worst of it passed in 2-3 days.
Much of the extreme tightness and discomfort lessened after treatments from my chiro, but it took many months to get it mostly resolved. There still was lingering neck tightness that we couldn't get rid of, until that one PT dropped my top ribs.