it seems there are 2 versions of the 13-3110M - there is a PGA version - which would allow for a replacement and a BGA version which would not. You would have to figure out which version you have.
Assuming you have the PGA version - the i5-3380M would appear to be reasonable choice (2.9 Ghz turbo to 3.6) but who knows if the mb supports it? - my guess would be yes. Look's like they are about $40 on ebay.
I don't know of any 'system information' software that will tell you which version of the processor your laptop has (pga or bga). The only reliable way to tell would be to disassemble the laptop and look to see if the processor is mounted in a socket (it could be replaced) or if it is soldered directly to the motherboard (it could NOT be replaced). Typically HP laptops are quite easy to tear down but ... I've no experience with this particular model.