Hi Customer,My name is Jane and I've been with Just Answer since 2006. It will be my pleasure to work with you. If you feel your dog has a gum infection, then it is very likely that there is a dental disease present. Since that is the case, your dog would need to be seen for dental care. Your vet can check for tumors, infection and growths. He can take care of cleaning the teeth and removing tartar buildup and prescribing an antibiotic to help clear up any infections present.
The following site goes over dental disease.
In addition, before giving your dog any prescription drug including antibiotics, your own vet would need to be consulted. I woud go ahead an make your dog an appointment. Now if there is no bleeding and your dog is in good health otherwise, aspirin might be used to relieve pain, but if you can get into the vet pretty quickly, I'd avoid it since other drugs might not be able to be prescribed without a waiting period if aspirin has been used. . Read side effects and precautions here.http://www.petplace.com/drug-library/acetylsalicylic-acid-aspirin/page1.aspx
Hope this helps you!