Before I had mine out (all 4 were impacted and HUGE) they hurt off and on for weeks. They weren't infected and when I finally got them checked out the surgeon said it wasn't urgent to get them removed, though it should happen eventually.
I got them taken out a few weeks later. It took a long time to heal and (I won't lie) the sockets hurt a LOT, but that's probably because I refused to take the hardcore pain meds, plus I had 4 huge ones taken out of my tiny jaw at once. I had a pretty big bruise on my face from where the surgeon had to pry my mouth open! I didn't get dry socket or an infection though. When/if you get them out, just make sure you follow the instructions the surgeon gives you and you'll be fine.
I'm not a dentist but if the wisdom tooth is completely covered by your gum I don't see how it could become infected. But even if it is infected, it's probably not serious. I think usually with infections you get something like fever and/or swelling, not just pain. Good luck!