Hi, I also have Graves (diagnosed in 2012). First of all, how is it possible you don't know if you have Graves?!?!? Your endo should test you for that. It sounds ridiculous to me he/she doesn't want to test you for it. If necessary, have the test done privately. It is very important to know if your hyperthyroidism is caused by an autoimmune disease.
When I was diagnosed I was extremely hyper (FT4 > 100; heart rate 196; not funny), but I quickly started to feel better on Carbimazole. My endo decided to give it a try (remission) after one year and since then I have been in remission (almost 2 years now). In the first months after stopping, I didn't feel well and had all kinds of hyper symptoms, and on top of that I had weird allergic reactions, low grade fever, and other strange symptoms. But every time I got tested, the FT4 and TSH were in range, so I just moved on and waited until I started to feel better. It took my body about a year to get "recalibrated" again, but now I feel fine, I exercise regularly, I eat well. I think your body needs to find its balance again. However, if your blood shows you're hyper again, then it's a different story of course.
I know some endo's test for antibodies before stopping the medication. They use it as an indicator to see how active the autoimmune disease still is.
Talk to your endocrinologist. You should get better care. All the best!