GLP-1s are not associated with papillary thyroid carcinoma, which is what I assume you had. In rats -- not humans -- it's been associated with medullary thyroid carcinoma, which is completely different.
FWIW, I have papillary thyroid carcinoma (have, not had -- I have not had surgery). It's the real deal -- Bethesda Grade VI, 2 cm tumor. I'm under active surveillance for it at Memorial Sloan Kettering and do not plan on having it removed unless it starts to spread, which it has not done in 6+ years.
I'm currently on Mounjaro, previously on Wegovy and then Ozempic. My doctors have no concerns with me being on a GLP-1.
That said, I had a lot more weight to lose than 10 pounds, so taking a GLP-1 was appropriate. For a 10 pound weight loss, I agree that it's not appropriate.
If you haven't already, you might consider discussing with your MD whether you have high levels of reverse T3 and whether Cytomel would be appropriate. I'm on Armour Thyroid which I prefer to Synthroid as well as Cytomel. We keep my TSH at less than 1, because that's where I feel best, but it doesn't make me particularly hungrier to be that low.
I agree that metformin might be worth a try, but it might also be worth consulting a nutritionist and personal trainer for additional help with diet and exercise.