Why did my charging system warning light come on?

The chime is going off to alert you to the charging system problem, have it tested.

i think you just need to get a new one

Have the charging system checked,Battery voltage(car not running) should be 12 volts,or less if battery is not fully charged.With engine running voltage should be close to 14 volts. use a dc volt meter and connect to positive and negative battery post.

could be a problem inside the alternator
you might want to have it bench tested at a store

Right now, I'm thinking the head lamp switch assembly has a problem? See the wire color in the top of head lamp, that is voltage, fuse protected, hot all the time. When problem is ongoing, you could use a test lite, check for voltage at fuse circuit?
The headlamp switch assembly is located on headlamp ground circuit. There could be a wiring problem, somewhere. I can only help with testing.

Replace the battery. The batter is on it's last leg and is about to die. The reason the light went off is because as you drive, the alternator provides charge to the battery. So the further you go, the more charged the battery becomes. That said, if the Battery warning light was on when you started the car, and you had not left any interior lights on over night, then the battery is losing charge rapidly or is not holding a charge.

Any car should easily recharge the battery after 20 minutes of driving. If your light stays on you could have a bad battery or alternator or both. Most part supply stores can check your system for free. One or the other being bad will wreck the other after just a few days, so I wouldn't wait to find out for sure.

Could be the battery also the alternator AutoZone does this check for free other places charge about 45$ to do that check

Belt broken. Do not drive!