You definitely need the B-12 and vitamin D... are you taking a sublingual or liquid vitamin B-12 of the methyl B-12? Methyl B-12 is "body ready", whereas cyanocobalamin has to be converted to methyl B-12 and we aren't all efficient at that. Sublingual and liquid is also more readily absorbed than pill types that have to be dissolved and absorbed in the gut, which is why most of become deficient in the first place - we don't absorb well.
Vitamin should be D3...
I'd ask for the correct antibody tests, as you've just missed your possibly diagnosis by not getting the right ones. If she refuses, it's definitely time for a new doctor.
I thought something looked funny. And you are correct there was no question about Graves.
My Vit D and B-12 looked like this....
B-12 267 (211-946)
D 37.4 (30-100)
Just last week, per her instructions, I started taking 2500 mg of B-12 and 1000 mg of D. Once a day for each.
What are your actual Vitamin D and B-12 levels?
Unfortunately, TSI does not test for Hashimoto's... To determine if you have Hashimoto's, you need Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb) - yes, both of them, because some of us have one or the other, some of have them both...
TSI is the definitive test for Graves Disease and I don't believe there was ever any question about your having that...
Your doctor is, apparently, not very will schooled in thyroid disorders; you might want to find one, who, at least, knows which antibodies to test for which condition...
your thyroid is fine
start supplementing for vitamin b12 and vitamin d and that will make you fine.