I'm so sorry you are going through this. I wonder sometimes if I still have some residual thyroid tissue left. I had my thyroid removed in a two step process last year (June and August), and 3 nodules were cancerous but not spread so I also didn't do any RAI.
I have Hashimoto's, and a total of around 14 lymph nodes were removed in the two surgeries - they didn't contain cancerous tissue but since my immune system was attacking my thyroid I presume they had some broken down thyroid cells.
Sometimes after a thyroidectomy, some pieces of thyroid are left where it attaches to the larynx/trachea at the isthmus. Some people can also have ectopic thyroid tissue, where bits of thyroid tissue are found not attached to the thyroid (I think this happens during embryonic development).
As for TSH fluctuating - I have no idea how that relates to what thyroid tissue you might have left. Mine has been all over the place in the last year (it was as high as 16 two months after my second surgery) and has taken a long time to come back down. Now I take liothyronine (cytomel), and I'm sure my TSH is bottomed out, although I still have some hypothyroidism symptoms (I'm doing much better now, but not quite "normal"). TSH is controlled by the pituitary gland, and is produced in response to the thyroid hormone in your body. I would think it has more to do with what you are taking than the amount of hormone any residual thyroid tissue might be making, but I guess that depends on how much hormone the residual tissue makes. Time of day and what type of thyroid hormone you take probably has a large effect on TSH levels.
How have they been monitoring for thyroid cancer/how did they detect they needed to do an RAI scan? Just ultrasounds of your neck? I've been having infrequent tests for thyroglobulin levels (blood test), and if that increases I guess that means thyroid tissue is growing somewhere in my body, but doesn't necessarily mean cancer since I might also have residual tissue. If your TSH has been high, I would assume the remaining thyroid tissue could grow a good amount. I've also had two ultrasounds on my neck (one at first appt Oct 2018, one August 201). I have no idea what he is looking for in that - I guess lymph nodes or residual tissue?
I too need to fire my endocrinologist and find a new one. He refuses to test for freeT3, he refuses to treat based on symptoms. I finally got my gynecologist to test for iron deficiency (or at least she tested hemoglobin in a full blood panel, and it was very low in its range, which was no surprise to me).
I feel like I have to be my own detective/advocate/doctor and I'm very thankful this site exists, because most of my doctors seem like as long as my TSH shows up "in range", nothing else that I describe going on is a problem.
I'm so sorry they have made you worried about the cancer coming back, especially if it is not coming back! If possible, you might try to get a second opinion, that might be a way to find a new endo and find someone who can clearly explain what they mean by residual thyroid tissue and how thyroid tissue might be in your lymph nodes but not cancerous.