Unfortunately, I think your little guy does need to see a vet. If anything, we need to get him on pain medications as we know pain delays healing. Beyond that, we need to make sure that no serious damage was done. Dog bites are like icebergs, often the damage is done under the skin and what we see on the outside is just the "tip' of the problem. Plus, dog bites can easily become infected. It is often best to stop the problem before it starts rather than wait until you have a big (and expensive) problem on your hands.
I hope that helps! Please let me know if you have any other questions!