Welcome to HCM,
In normal condition if adequate amount of thyroid hormone are produced the TSH
is suppressed by feed back,but if Thyroid gland is under active due to any reason then more TSH is released and it level rising is very good test to diagnose Hypothyroidism
,once this is supplemented in the form of tablet Eltroxin
this TSH value will become normal .
Hypothyroid is common ly due to autoimmune process, but it can be due ti other causes as well like surgery,malignancy.
is high indicate infection and use of antibiotic depend on site of infection and organism involved if it is not working please visit Physician again to asses the condition and if any further testing is required or suitable antibiotic may be required.