I too am not avid for iodine and have detectable Tg (and TG antibodies). In my case, Tg never went all the way to zero after the RAI and once it started rising, we did a small dose of RAI to see if it would take up - it didn't - but we knew something was going on because I had rising Tg. Next step was a PET scan which showed nodules oustide of my neck. I agree with the above posters - it's critical to be managed by someone who is very familiar with thyroid cancer, better yet with atypical cases of thyroid cancer in cases such as mine, and perhaps yorus.
I get Tg checked every four to six months and since the start my doctor has insisted on sending my bloodwork to USC for this particular test, especially because I have antibodies (they mess with the Tg level, as you may already know). USC banks previous samples and reruns your last one on the same day as the new sample. This allows for greater accuracy - same assay, for example. If you have antibodies, my understanding is that it is extra important to have your Tg labs done at the same lab every time so that they are comparable.
Best to you and please let us know what your docs recommend next. Don't wait though - ask about the plan of action and reasoning. A good doc will go over all of that with the patient. My endo has been very good about going over options, rationale for the plan etc.