Swelling from excessive licking usually goes away when your pet is prevented from bothering the area with a cone collar.
Apply an antibiotic ointment a few times a day, as long as your dog is not licking it off.
Your vet may prescribe pain medication or an anti-inflammatory to relieve the discomfort until the inflammation goes away. For dogs, you can usually hide pills in a tasty treat. For cats, you can try crushing the pill with the back of a spoon and mixing it into strong smelling cat food.
In cases where swelling is caused by infection, you will need to give antibiotics for up to 2 weeks as prescribed by your veterinarian after diagnosis. Signs of infection include fever, discharge of pus, loss of appetite, lethargy or hiding behavior, and constant licking of the area. The area may be red or discolored and painful to the touch. If you suspect that the infection has turned into an abscess, and there is an open wound with a red discharge of pus, have the vet re-examine your pet.
In rare cases, the swelling after neutering becomes so severe that it leads to damage of the scrotum. In these cases, a repeat of the surgery or the insertion of a drain may be needed. Clean the incision and drain area as needed with sterile saline contact lens solution on a gauze pad.