My Husband Was Bit In The Hand By A Boxer/American

My husband was bit in the hand by a boxer/American bulldog on Monday night and the owners said the dog has had all of his shots. It seems to be healing fine and we washed it well a few times right a way and again a short time later. We have used neosporin and regular band-Aids and kept it clean. Is there any reason for him to see a doctor if it is healing well? Our small dog was also bit and she developed an infection that is now under control.