Yes,in looking closer and with what you typed, it is Free T4, not Ty. I do not see Free T3 on the lab request and I will ask about that. As my doctor is very well respected and sought out in the community, I am not sure why T3 is not on the lab request. I know that there was blood work before the surgery. I will ask. I just started asking for copies from my file, i.e., hospital report of my thyroid lab work which is how they found out I was Hashimoto. Again, no symptoms whatsoever to suggest thyroid problems. Only reason I ever went to the specialist three years ago was neck ache and earache. Benign needle biopsy three years ago, but with change in nodule size, the doctor felt it best to do another biopsy, thus the indiscriminate cells, the need for surgery, and the discovery of Hashi with Hurthle cell changes which were benign.
Hashimoto's is an autoimmune disease, in which the antibodies gradually destroy your thyroid and it will eventually no longer produce hormone. It's likely that at some point in your life, you will be totally dependent on some type of medication to replace the thyroid hormones that your body needs.
You said you are going for TSH, free Ty (what is that? or is it a typo?). You need to have Free T4 AND Free T3 tested. Many doctors will willingly test FT4, but most refuse to test FT3 -- insist on it and if your doctor refuses, I'd suggest finding another.
Noting your age, the "symptoms" you have - hot flashes and chills - could be from menopause, also.
The important thing will be to see what your Free T3, Free T4 and TSH levels are. When you get the results, please post them here, along with the lab's reference ranges, since labs use various ranges depending on the method used to analyze the sample. DO make sure you get a written copy of the lab report for your records.