There's another antibody test you should get to determine if you have Hashimoto's. It's called Thyroglobulin Antibodies (TgAb). Both TPOab (Thyroid Peroxidase Antibodies) and TgAb are markers for Hashimoto's and since your TPOab was negative, you could be misdiagnosed by not having the other test.
You also need to be tested for Free T3, along with the TSH and Free T4. Free T3 is the hormone that's actually used by individual cells, whereas Free T4 is considered a pro-hormone (or storage hormone) that has to be converted to T3 in order to be used by the body. Be sure to test Free T3 and Free T4, as those are the portions not bound by proteins, and can actually be used/converted.
All of that said, your TSH is lower and your Free T4 was at the very top of its range, indicating that your thyroid hormone levels may be too high. Although it's true that replacement hormones can help shrink nodules, I'd wonder about prescribing additional hormones when levels are, possibly, already too high, which is possibly why you had trouble taking a whole 100 mcg.
Although Hashimoto's is, typically, characterized by Hypothyroidism, early stages can often present with periods of hyperthyroidism (too much hormone), alternating with hypo or normal periods. Hashimoto's can also be diagnosed, based on characteristics of the thyroid, as noted on ultrasound, so check the ultrasound report and see if it mentions anything about characteristics being consistent with Hashimoto's.
Nodules are very common with thyroid conditions, both hyper and hypo, as well as Hashimoto's and/or Graves Disease. Very few nodules are anything to worry about - less than 5% turn out to be cancer. Since you had the FNA and your nodules were determined to be non-cancer, they aren't a problem, unless they're causing swallowing or other problems. I've had a "moderately suspicious" nodule for several years and nothing has been done with it, as it's been considered too small.
Nodules can also be shrunk by using Radioactive Iodine (RAI), sometimes without surgery or replacement hormones.
You need to find a doctor willing to run all the pertinent tests in order to figure out exactly what's going on.
Has there been a cause determined for the excess estrogen and/or low progesterone and testosterone? Has anyone suggested you may be beginning peri-menopause? The reproductive system, along with the adrenals are part also part of the endocrine system and all hormones need to work in sync in order for us to feel best. Some reproductive hormones are produced in the adrenal glands. Cortisol levels can affect levels of other hormones. The pancreas is also part of the endocrine system, so insulin and blood glucose levels can also affect other hormones.
Trust your instinct and get a second opinion. A thyroidectomy is a lifelong decision so weigh all options/risks carefully. A surgeon that won't share results seems very dodgy. I would stay away. The dr should determine what is causing the goiter, recommend a treatment plan and give it time to work. Good luck!