Battery draining in 2 hours after using generic charger

I bought a generic Mini-USB wall charger off eBay and plugged it into my phone.  As soon as I did, the phone started behaving strangely.  The interface would lag and the touch screen could barely interpret any of my input.  I left it charging for a couple hours because I really needed to charge it.  It started getting a little warm so I unplugged it and haven't used the charger since.  The problem now is that the battery discharges in about 2 hours even with little to no usage.  Also, the phone itself becomes warmer than usual when plugged in to the OEM charger I purchased as a replacement to the generic.  I figured the charger destroyed my battery so I replaced it with a new one, but I'm still having the same problem.

So my questions are these:
1) Did the generic charger permanently damage the hardware in my phone so that I must now replace it?
2) Is it possible that the issue is due to corruption of the phone's power management software and that it could be resolved by a factory reset?
3) Are there any possible fixes you can think of?

Despite its shortcomings, I like this phone and would rather not replace it.  However, I am due for a discount with a 2-year contract renewal with Verizon and am open to replacing it if there are no other options available.

Thanks in advance for any assistance you can offer!

TL;DR - I plugged my phone into a generic charger and now the battery drains in about 2 hours.  Battery replacement and new charger did not fix the issue.  What now?

I actually performed a factory reset last night and saw that my battery life, while not as good as when I originally purchased the phone, has been extended by about 6 hours and the device is no longer running hot.  So I think you're right that there was something wrong with the calibration of the battery with the current software that a reset has resolved.  Thanks for your advice!