Get to an ENT. You should be able to get into them and they will be familiar with abnormal thyroid function. They will do the full works on your boy or should. This is rediculus. The other option is an allergist immuneologist. ENTs tend to be a bit easier to get into though.
He needs the following checked for his thyroid:
TSH (sensitive/3rd Gen)
Blood chemistry and immunity panel would be good as well.
IgA, IgG, IgM, IgE.. etc.
I am leading to the ENT to get you into an ENDO and evaluate things now for you. They will be able to rule out throat infection in a quick visit and not drag there feet like your current MD.
Depending on the thyroid panel results adrenal/pituitary function may need to be checked. Hang in there. My son is fine, but I developed Hahsimoto's during his birth. My son has of late been diagnosed with sleep apnea.. just like his mom and dad.. chronic sinus and ear ills. Like mommy and daddy.
The new kicker he has developed or has immune deficiency in IgG and IgA. These are the immunities that work in the sinus cavities. Anyway.. having both is also a known precurser to AI issues. SO.. we watch and test and are glad my son at 5 yrs has good veins and like MDs. He prefers shot free MD zones. Sleep MDs have a bed to jump on and no shots
. ENTs are not bad, because he has only had IVs after being doped up for his Tonsillectomy and adenoidectomy. It will be okay, but you can not trust a pediatrician to do more than basic care and treatment. GO to the specialists that handle children for the rest. Get copies of EVERTHING and double check EVERYTHING.