Need Help with phone!!!!!!

Hi guys, im new to the forum and its such a good one to explore for android in general :)

So I got this Galaxy Y and for 1 week it was OK.Phone was working great.Then after that, phone started to shut off randomly when Im using it and especially when it is in my pocket :s (I go out, have a walk, when I take phone out of pocket... its has shut off)

I dunno what to do.I tried factory reset a FEW times but no success, also downgraded to 2.3.5 (it was 2.3.6) but again same issue.Tried software update also but still same problem :(

Also when I charge the phone to full, it shuts off, I turn it on and battery has gone very low.

The only option its to get a new battery!!??

Please Help guyss.... :(