I am not a medical doctor, but I had multiple thyroid ultrasounds last year (and multiple thyroid surgeries).
First and foremost - most thyroid nodules are benign (90-95%). Current guidelines recommend a fine needle biopsy for nodules larger than 2 cm (sometimes larger than 1 cm if they meet certain criteria). The fine needle biopsy will tell you whether your nodule is benign, indeterminant (suspicious for neoplasm is indeterminant), cancer/malignant, or sometimes the result comes back "non-diagnostic" where they just don't get enough cells to determine whether it is benign or not. Chances are good that you will need a fine needle biopsy as your next step, but at this point it is impossible to determine whether it is cancer or not.
I'm unfamiliar with thyroid cancer rates among people with Li-Fraumeni, but as far as the general population, thyroid nodules are very common in women and don't necessarily mean they are cancerous. I was told by my endocrinologist that 20% of 20 year old women have nodules, 30% of 30 year olds, 40% of 40 year olds, etc. In most cases these nodules are benign. A quick google tells me thyroid cancer may occur in people with Li Fraumeni, but the risk is lower than the "core cancers", so your risk may be higher than the general population, but still does not mean your nodules are cancerous.
If your nodule is cancerous, most thyroid cancers are usually slow growing and very treatable (depending on your age and how far it has spread). If your nodule happens to be cancerous, treatment usually involves at least the removal of the thyroid lobe containing the nodule. Depending on the size of the malignant nodule, if multiple nodules are cancerous, or if there is evidence of spread, you may need a full thyroidectomy and possibly treatment with radioactive iodine, but at this stage you just have some nodules that you need to get checked out by fine needle biopsy. (I had one nodule that was suspicious for neoplasm by biopsy, three nodules of about 1 cm each that ended up being cancerous after a thyroid lobectomy, and then a second surgery to remove my other thyroid lobe and isthmus which had several large nodules including one 2.8 cm nodule and one on the isthmus, none of those with cancer, and I was lucky that my papillary thyroid cancer hadn't spread and I didn't need RAI.)
Have you been tested for thyroid hormones and thyroid antibodies? Your thyroid is increasing in size and the nodules are growing, which makes me think that you might have higher levels of Thyroid Stimulating Hormone (TSH) which encourages thyroid growth, and usually signifies a thyroid problem like hypothyroidism (often caused by the autoimmune disease Hashimoto's). If you haven't been tested, I would get your thyroid antibodies tested (which would tell you whether you have Hashimoto's or Graves diseases) as well as TSH, freeT3, and freeT4. (T4 is the main thyroid hormone produced by your thyroid, it gets converted to the active form T3 throughout the body, and if either of those is too low it could signify a problem). If you do have elevated levels of TSH or hypothyroidism, treatment for hypothyroidism may slow down the growth of the thyroid and nodules, since TSH stimulates thyroid growth, and it is important to get that checked out even if your biopsies come back benign. (In my case I had "subclinical hypothyroidism" and I ended up with a multinodular goiter due to chronic untreated Hashimoto's that I didn't know about until too late).
Alternatively, Li Fraumeni syndrome might be stimulating thyroid growth in some way and your thyroid hormones might be fine, but I'm not sure why the whole thyroid would be increasing in size if that were the case. Maybe this is something to ask your oncologist or cancer specialist about - it is outside my very limited thyroid knowledge.
I'm so sorry you have to go through this - if it is thyroid cancer it is treatable and lots of people on here have had thyroidectomies and are doing well.
Good luck, I hope you can get biopsied and get some answers soon. Hopefully it is not cancer, and there is no reason at this point to conclude that it is, just that you need to have a biopsy done.