Sounds ok, but . . .
A person with muscle tightness and/or muscle aches can be checked by a rheumatologist, but the better way to get evaluated is to see the primary doctor first.
Many disorders can cause muscle tightness and aches/pains. Blood tests can be ordered by the primary doctor. If rheumatologic diseases (autoimmune disorders) show up on exam or on lab results, then the rheumatologist can be consulted.