My chiropractor said to go to a rheumatologist and get tested for blood disease for muscle tightness. Does that sound right?

Yes. A rheumatologist is an expert in inflammatory & non-inflammtory muscle disease and can guide you to the proper physican to deal with the problem, if they cannot!
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.