I was diagnosed with Graves too, did the radioactive pill too, and also had the episodic shakiness/accelerated heartbeat for a long time. Thyroid tests said all was well with the Levoxyl dosage. In the past blood pressure always low, now often high. Tendency to gain weight. Doc tried blood pressure meds which made me sick as a dog. About 5 years in severe aching joints set in. Doc said 'Oh, it's probably just arthritis - here have some pain pills.' ( I declined the pain pills) This pain went on for about two years getting worse by degrees.
Cut to the chase - when the dosage was lowered all this cleared up. In 45 days I felt better than I had in years. Shakiness/accelerated heartbeat went away. About eight months after lowered dose the joint pain decreased bit by bit. Took two and a half years for it to go away entirely. And by the way the circular that came with the medication says to contact your doctor if joint pain sets in. Duh...wonder how we got into an opioid crisis.