This can happen - stopping the synthroid is the best way to sort it out and see if you have recurrent hyperthyroidism that needs anti-thyroid meds or I-131.
If your doctor were to run both the TSI and TPO antibodies tests it would indicate what is happening.
There is a thyroid disease called hashitoxicosis which is both Graves and Hashimoto's happening at the same time. The symptoms that present with whatever antibody is dominent at the time. It's very difficult to get a diagnosis for hashitoxicosis because many graves patients have both TSI and TPO antibodies present, you however, have had both hyper and hypo symptoms so it sounds likely to be your issue.
It can be difficult to treat because the patient is always going back and forth on symptoms.
Read up about it on the web so you can have questions prepared to ask your doctor.