I'm not sure where you're getting your information, but any notes on thyroid function and/or thyroid testing must include information on Free T4 and Free T3, which are the actual thyroid hormones, not just mention of TSH, which is a pituitary hormone that does not always correlate with actual thyroid hormone levels or with symptoms of a thyroid condition.
I suspect the "infection" you're referring to is inflammation caused by an autoimmune condition?
In most cases, thyroid antibodies (TPOab, TgAb or TSI, depending on the situation) should be tested, since autoimmune condition can be present, causing inflammation/swelling and/or other symptoms, long before actual thyroid hormone levels go out of range. In addition, lab ranges are set in such a way, that those with levels in the lower portion of ranges for Free T4 and Free T3, almost always have hypothyroidism, even though doctors refuse to make the diagnosis. On the flip side, those with levels in the upper portion of the ranges can be hyper, but still considered "normal", as well.
In most cases, a thyroid ultrasound is also called for to determine whether or not the patient has nodules. Nodules are, typically, benign, but they can be cancerous, or in the case of hyperthyroidism, they can produce thyroid hormones, independently of the thyroid.
It's not the least bit hard to diagnose a thyroid condition; med schools need to change the way they teach the chapter on thyroid to include proper/thorough testing/treatment, with more reasonable reference ranges. Secondly, doctors need to change their attitude toward patients and understand that we know our body better than they do. They need to understand that the majority of us are not the hypochondriacs they suppose we are. Whenever thyroid related symptoms are presented (in most cases, even one thyroid related symptom should qualify), a thyroid condition should be ruled out/confirmed, with a full thyroid panel, BEFORE other things, rather than left as a "last resort" thing to look at.
It's very unfortunate that many/most doctors are way too willing to blame depression, fibromyalgia, eating too much, poor diet, lack of exercise or a myriad of other things - it's always the patient's fault, even when it's not...but they don't want to blame that poor little gland in our throat that defaults way more than they admit.
"However, unless the doctor gets the thyroid numbers to coordinate the finding, it's hard to accuse the thyroid." With the increasing prevalence of thyroid disease in today's world, it's not the least bit hard to accuse the thyroid of any number of malfunctions. Any practitioner that fails to get those thyroid numbers right off the bat, is doing a great disservice to the patient.
All of that said, welcome to the forum...