Hello Dear. First of all, your situation seems a bit more than most people know what to even suggest. I felt compelled to respond because I know what it is like when there seems to be "no answers." I am not familiar with graves disease, but I think I recognize some of the other symptoms. I imagine you may be on some meds for the graves/thyroid conditions, right? Those meds may actually be INCREASING your upset simply because of the nature of the meds. Read the side-effects sheets that come with ALL meds.
I said I recognized some of your upset symptoms...have you ever had you're gall bladder checked? It can cause a lot of mischief if you have gall stones. (2 of 4 of me and my siblings had ours removed. I had a lot of the same symptoms you described..stomach upset..vomiting, couldn't lay down because I would wake up choking in my sleep, diarehia,...) The "cold sweats" are probably more associated with your other circumstances. If you are having persistent issues, I would DEFINATELY talk to your Doctor. I have done home health care for 9+ yrs, and there are MANY alternative meds..more and more each year. These seem like pretty life interupting symptoms and your Doctor is one of your BEST resources. I'd also suggest finding a support group...if you're unsure where to find them, just google it. (I had one ONLINE...we were all in different parts of the world, but dealing with the same doubts, fears...triumphs.

Good Luck my dear! God Bless!!!