Keep his fingers clean, that's your biggest danger. The skin might peel and you'll need to keep the germs out.
Other than that, I would't worry. There is nothing a doctor can do for you unless he requires a skin graft or has an infection. If he's not feelng pain then just put a bandaid over it to keep the germs out for the next few days (change when it gets wet) and he'll heal just fine. If it starts to ooze pus and stink while turning an angry red, then take him to the doc as that means infection.
His body is an amazing thing. I am betting this hurts you more than it hurts him. I hope he heals quickly