We need to know the reference ranges for the Free T3 and Free T4. Ranges vary from lab to lab, so have to come from your own report.
Your FT3 and FT4 do seem pretty low, which would be consistent with the elevated TSH, but, of course, that does depend on the ranges.
It's unlikely that the tonsillitis is related to the thyroid issue, but anything is possible. If your thyroid is swollen/inflamed, it could "feel" like tonsillitis. When my thyroid was swollen/inflamed, I felt like I was choking all the time.