I was in a car accident, I was diagnosed with thoracic outlet syndrome. What can I do next?

Manual Medicine. Aside from anti-inflammatories; and rest you should find a good osteopath as he/she can treat this easily. Otherwise you may need some physical therapy and possibly further evaluation...Check in with your doctor about this.
Conservative Rx. In my experience, 85% of all tos pts can be stabilized with conservative treatment. This includes pt, exercise programs, chiropractic, etc. Feldenkreis postural therapies can be dramatic, if the prior fails. Surgery should be delayed until clear that all else has failed. Selection of candidates for surgery can be based on arteriography and/or brachial plexus emg.