Condoms are great as far as keeping people from getting STD's if used properly. You did check it and there were no holes or tears. It could be the brand of condom that caused irritation. You can get checked for your own peace of mind but since you did not have a condom failure I would say you're fine. If the irritation is there tomorrow get in to see your Dr to find out if this was an allergic reaction to the condom. If so, they can prescribe an ointment for it.
Honestly I believe u should get tested! There's going to be a moment where u will want to be intimate with your girlfriend and the poor girl has no reason why to catch something when she hasnt been with anybody else but you and ull most likely end up getting caught this way if she has to visit her doctor for this tingling sensation you are feeling at the moment. It could be your guilt but I say better safe than sorry!!!