Kitty cut his paw pad, limping

My kitty Oliver burned his paw on my stove the other day when he jumped up on it by accident. I ran it under cold water and and continued that for a while. That was two days ago and he was constantly licking it. I came home from work today to see that he was limping. I looked at his paw and one of his pads was cut and sore, which I'm assuming is from his constant licking of the old burn. Is there any sort of ointment I can put on the cut to make it feel better for him? Do I need to bandage it up at all? (it's not too terrible) Just looking for some tips from someone who has maybe had this happen to their kitty before, thank you! :D

Put some antibiotic ointment on it - Neosporin has a version that has a pain killer in it. You really should see a vet so they can clean it properly and give him the proper treatment.

Oh, poor Oliver, it must be painful. I think Redhedd's suggestion sounds good, and he keeps licking it, you better take him to the vet.

When you get burned, it takes a lot of time before the pain goes away. I once burned my finger on the oven and had to sit with it in a glass of water for about two hours. I was also burned very bad on e time and ended up in hospital for 5 weeks, there they said the best is to stay in cool water - not ice cold and not running water, for as long as it takes.

Hope Oliver will feel better soon! :)