If your son's bite was something that would spread or was very toxic (such as a brown recluse spider for example), he would have had worsening symptoms the first day. Most likely this is not healing because it has gotten infected.
To treat it at home: wash the area with warm soap and water, dry well. Apply an antibiotic cream you can get over-the-counter at your local pharmacy and rub this in well. Because he is young and probably puts his hands in his mouth all the time, you want to make sure it is fairly well absorbed. Then try to cover it with something. I think a bandaid he would probably pull off and try to eat it. So you might have to forego a covering and just treat it about 4 times per day. If you can keep it covered, you only need to clean it and apply the cream twice a day.
Use antibiotic cream, not ointment. The ointment will leave a film on top of his skin that he can lick off.
If you do not see improvement in a couple of days, you should take him to his pediatrician. Children are very prone to getting skin infections that get infected with bacteria, which could get worse and spread. The at-home treatment should work OK, but if not---make sure he gets to a doctor, especially if the area gets larger, develops redness around it, starts swelling, or more red spots appear around it.