I opened up my laptop to see why the fan made weird noises, and found the battery looking swole.

Could this be connected to my fan issues? The fan appears to start normally, then starts vibrating aggressively while slowing down, then sometimes transitions to normal operation again. Here is a video that shows the issue. When the ugly noise happens, the fan slows down noticeably. This only happens when not charging. When the laptop is plugged in, it works fine. I have removed what little dust there was in the fan, and ordered a replacement fan.

Do I need to replace my battery as well? It's significantly more expensive, but it's worth it if the alternative is a dead laptop soon. I really cannot afford to be without a laptop.

Here is the output of the "inxi" tool:

./inxi -Bxxx
Battery:
    ID-1: BAT0 charge: 11.5 Wh condition: 28.9/35.3 Wh (82%) volts: 10.8/11.4 
    model: Notebook BAT type: Li-ion serial: 0001 status: Discharging