I have the same issue with my battery as well. It's swell up as well.
The phone would work fine if it's plugged in.
First I had the problem is when I had the battery at 100% and suddenly after using it for only 15-30 min the phone rebooted and when it's back on it's only at between 3-5% and it says to plug it in to a power source. Even restarting and taking of the battery it would show the same thing. But when I plug it in and restart, then it would show about 80+%.
I change the battery to amazon third party and never had the same problem.