I would say wait till you are better, you should not do bloods while you are poorly, I am not sure about the antibiotics affecting results but any infection should be over, or you will need to do a retest.
Some people advice waiting 12 weeks after a dose change so this may be better all round for you hopefully you will be well over the infection in another 4 weeks,
Any acute infection can affect your thyroid results, it is recommended to wait until a few weeks after the infection has cleared before doing a thyroid test otherwise you cannot rely on the results being accurate.
I would wait a couple more weeks at least if you have had an infection or have been unwell with a cold or Virus. When looking at when my routine blood tests were taken pre COVID pandemic, they always coincided with a GP visit or a few days after for either an infection or generally being unwell, nearly every time it resulted in a dose change up or down. I would see the GP and whilst there they would say you haven't had a TSH check lately and that would be it.
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