Suspect inflammation of a muscle. what kind of doctor should i see?

Primary care : For "inflammation of a muscle" I would recommend that you start with a Primary Care Physician such as an Internist or Family Practice physician. They can take care of the majority of musculoskeletal complaints. They will refer you to an orthopedic surgeon if needed.

Your generalist: Your primary care physician will decide if there is a need for a specialist. Most muscle conditions are self limited, while few might need specialized care, including a possible biopsy.