You have to have all the antibodies tested. TPOab and TGab are associated with Hashi's. Only one has to be elevated to confirm, so both have to be tested to rule out. TPOab is actually the more common one associated with Hashi's. If they were only going to test one, they picked the wrong one.
TSI is associated with Graves'. And, yes, this one is necessary, too.
I feel that labs are getting very sloppy. It's not just labs; it's imaging centers, too. Reports use a lot of discrimination values, so in the end, you don't know what your result really was. As a snapshot test, it's not that important...a "less-than" or "greater-than" value is fine. However, if you have a series of tests over time and want to compare, it's almost impossible.
You originally posted your TGab result as "less-than 1.8". Was it "less-than 1.8" or "1.8"? If it's "less-than 1.8", then the lab is using discrimination values, and your result could be anywhere from zero to 1.8. Either way, no, I wouldn't call your TGab elevated. Bear in mind that those of us with Hashi's often have antibody counts in the high hundreds, or even thousands, on diagnosis.
TGab tells you nothing whatsoever about your thyroid function. We can have antibodies for years or decades before they damage the thyroid enough to cause out-of-range labs and symptoms. All antibodies really tell you is that you have the potential to develop thyroid disease. FT3, FT4 and TSH (if it's reliable in your case), tell you if your thyroid function is normal or not. The general rule of FT4 is that it should be about midrange. We don't have your range, but 1.47 is a little above most ranges' midpoints. FT3 should be in the upper half of the range. Yours is total T3, but you can see that it is above range, which could be making you feel hyper. However, your TSH is not suppressed, which would indicate that your pituitary is pretty happy with your levels.
Thyroid eye disease typically goes with Graves', not Hashi's or postpartum.
A nodule is a small overgrowth of thyroid tissue, you can't usually see a nodule. As you can see, yours is only 10 mm. A goiter is an inflamed, swollen thyroid. It can be visible if it's big enough to distort the neck. If your thyroid was reported on U/S as normal in size, you don't have a goiter.
First of all, unless your U/S report contained other information that you didn't post, a thyroid nodule is different from goiter. A nodule is a small overgrowth of thyroid tissue and extremely common. A goiter is the overall swelling of the thyroid. It's not necessarily a warning sign of hyperthyroidism.
Your total T3 is above range, but FREE T3 is a much more informative test. FT4 does look a little high in the range, but not above most ranges. Ranges vary lab to lab and have to come from you own lab report.
Your doctor should test TSI (thyroid stimulating immunoglobulin), which would tell you if you have Graves' or not. TPOab (thyroid peroxidase antibodies) should also be tested. They can be elevated with both postpartum thyroiditis and Hashimoto's thyroiditis.
A goiter is not the cause, but the result, of thyroid disease. Once again, did the U/S report mention a goiter (enlarged thyroid)?