This might be a sign, Jake, of developing TED. If that is the case, you might want to see your doctor and revisit the decision for RAI. The current theory is that RAI can aggravate — specifically make temporarily worse — any TED. Studies have shown that if you take a concurrent dose of prednisone with the RAI that TED is not aggravated. So when TED is present in any significant degree, our doctors either suggest surgery (which is not shown to aggravate TED) or the prednisone, if it is thought the person can tolerate it. So, if you have doubling of your vision, you need to get it checked by an opthamologist, in addition to talking with your endo.
I do know how awful it is to have double vision. I took to wearing an eye patch at times. The patch works to eliminate the double vision, but it also eliminates depth perception, so it makes driving a bit more hazardous. Of course, driving with doubling is hazardous as well, so I stayed off the roads for a long period of time. Or drove back roads with little traffic. And be sure, if you do this, to alternate the patched eye so that you don’t weaken one.
