Which type of doctor should i see for a rotator cuff problem?

Sports medicine or : Shoulder specialist.

Sports Medicine: Musculoskeletal Specialist or Orthopedic Surgeon.

Orthopedic Surgeon: An Orthopedic Surgeon is very capable of examining and diagnosing your rotator cuff issue and determine which kind of treatment is indicated first. More times than not, a RTC problem at your age can be treated conservatively. Typically, physical therapy will suffice in the beginning. However, if your physical exam is more concerning, then a MRI or an injection may be indicated.

Depends: If you have not had an acute injury and have not had any non-operative care for the shoulder you could either see sports medicine or your primary physician. If you have had an acute injury and have failed non-operative treatment I would see an orthopedic shoulder specialist.