Should I have a follow-up PET scan a year after diagnosis of HCC

In July 2022 I was diagnosed with Hurthle Cell Carcinoma (HCC). I had a PET scan a few months after the surgery and the report stated there was uptake in the neck region “probably due to swelling.” I did not like to read “probably,” after my surprise of diagnosis of HCC.
I had to go on Synthroid about 3 months after surgery due to increasing issues associated with thyroid disease. I am having a very difficult time getting the Synthroid regulated and seem to have a lot of concerning symptoms. I understand that the issues could be related to other issues and part of the process for finding the right Synthroid dose, however the symptoms are also consistent with HCC.

My surgeon had submitted my right lobe with the large nodule for biopsy, but did not submit any lymph nodes, or the parathyroid that was mentioned to be “looking very bad.” Since I seem to be having some of the same symptoms as HCC and can’t get my Synthroid dose regulated so the symptoms go away, I requested a follow-up PET scan to make sure we aren’t missing something. The doctor said that since my thyroglobulin is low, it isn’t thyroid cancer. My Thyroglobulin antibody is high, however the notation says the low thyroglobulin can’t be used to rule out cancer because of the high thyroglobulin antibodies. I thought a follow-up PET scan would rule out HCC as a factor for some of my symptoms, however doctor just says that my thyroglobulin is low so it isn’t thyroid cancer. I am curious if this number would be raised if the cancer had gotten into my lymph nodes or other regions…I will be researching that later.

Has anyone with HCC had a follow-up PET scan a year after surgery? Is there a reason to request one? I know that I am overly concerned the doctor might be missing something due to the surprise of this diagnosis after being monitored.
Thanks!