Please post the actual results with reference ranges, since simply being in the normal range, is often not good enough. If your levels are too low in the range, you still won't feel well.
Was it Thyrglobulin (TG) that was high, or Thyroglobulin Antibodies (TGab).
Rescent (first test) results: TSH, T3 and T4 - all within normal references ranges, but Thyroglobulin was high - 101.0 (range <60 ng/mL)
Yes, the nodules could contribute to hoarseness. Hoarseness is a very common symptom of hypothyroidism.
Have you been tested for hypothyroidism and Hashimoto's Thyroiditis? Are you currently on any thyroid replacement hormones?
If you have current thyroid labs (should have at least TSH, Free T3 and Free T4), please post the results, with reference ranges, which vary lab to lab and must be posted with results.