The gum around a tooth is infected and maybe in my sinuses too. should i visit a dds or md?

Possibly both: I would certainly recommend that you have your dentist evaluate the area first. They can help identify if it is a dental infection or problem or a combined dental/medical problem. If it is, they will refer you to your physician to co-treat the problem.

Probably a DDS: A dentist can handle a gum infection and a normal sinus infection. However, an md probably won't be too proficient at treating a gum infection. So, it seems logical to me to start by seeing a dentist. If you need to be referred to an md, your dentist can do that for you and also follow-up properly.

Possibly both: Since you mention that the gum around a tooth is infected, that is clearly in the purview of a dentist. A sinus infection that occurs as a complication from a tooth extraction can be well-managed by an oral surgeon. A sinus infection should otherwise be evaluated and treated by a physician. Notably, a maxillary sinus infection can often masquerade as a toothache.

Both...: Simple test. Sit down, bend over, put your head between your knees. If pain increases, sinus is involved. Ask your md/do to refer you to and ENT specialist. If gum around a tooth is sore, may be gum disease, abscessed tooth, fractured tooth, hyper function, or one of many other dental problems. See your dds?Dmd for rx or referral to periodontist, endodontist, or oral surgeon.