If you bought the laptop new a couple of months back, it should still be in warranty which would entitle you to a new battery - surely!.
Now the difficult part, if you bought it with Windows installed, the supplier wouldn't be too keen on replacing it as they are likely to say you've invalidated he warranty by installing Mint.
I've never understood this as they're generally loath to sell you the laptop without an OS on it anyway! It's the hardware that's suspect, not the OS!
If it was bought in a store with a repair facility they might be able to let you leave it with them with a "replacement" battery fitted to prove if it's faulty or not. If it is, you should be able to have it replaced.
(I'll now wait quietly so that others can tell me how difficult/impossible this will be!!