Battery polymer film ripped: safety concern

A few weeks back I was replacing my friend’s old iPhone 6’s battery. The adhesives strips ripped apart and I was unable to remove it. Then, I used a hair dryer to heat up the chassis and in turn heat the adhesive. I was using a pair of relively sharp pair of tweezers and punctured the battery (the side stuck to the adhesive). I did not notice this till the battery was completely off. I also ripped the chips on the battery in an attempt to get to the adhesives.

Once the battery was off, I placed the damaged battery in a small bag but left it open. About an hour or two later my nose, mouth, my eyes and my throat started to “burn”. I looked at the battery and saw the black film was ripped, punctured, or otherwise absent in two spots of the battery. The places where the film wasn’t showed a silver surface underneath (which I didn’t touch). On the side which was not compromised, there were spots of the film coming up, which was compressible (like there was air underneath it). The battery was also slightly bent. During this entire time, the battery did not spark, heat up, smoke, or even smelled like anything. (As far as I’m concerned, no liquid leaks)

So my safety concerns:

Am I going to be fine?

Should I be concerned about the dust around the area of my desk where I did the operation?

(Note: my hands don’t burn, and the “burning sensation” left after the next day)

I am willing to give more information if need be.