Why did my battery filled with air?

It is not uncommon for lithium ion batteries to swell as they age. The electrolyte inside that carries the current begins to decompose and that process generates gas causing the battery to swell up. It's an unfortunate fact of life with Li-Ion batteries as they get old and near the end of their life.

What you don't want to do is to puncture the membrane to "let the air out". That can easily cause the battery to catch on fire, and believe me, lithium burns very well and very hot, so you don't want to do that. Remember the Galaxy Note 7?

Ultimately you may have to disassemble the camera far enough to be able to get the old battery out without damaging it. If you have to deal with a swollen battery, be sure to take precautions against the chance of it catching fire; a bucket of sand or a fireproof pouch would be good to have on hand. DO NOT put it in water; that will just make things worse! Here's a Wiki article on dealing with them that is well worth your time to read.

What to do with a swollen battery - iFixit