Do you know what the reference range is for the t4? It could be low or high depending on the lab. Reference ranges vary a lot from lab to lab.
I suspect your t4 is actually at the low end of the scale, hence your high TSH. If your tsh is approaching 10 it means your thyroid isn't producing enough t4 and t3 and that is likely why your doctor wants to reduce the carbimazole further.
Ideally you want your TSH below 3 and your t4 in the upper part of the range. It sounds like the carbimazole is still suppressing your t4 production too much and this is why your TSH is rising. A further decrease should hopefully allow you t4 level to rise which should then cause your TSH to drop. If this doesn't work, your doctor may stop the carb altogether. If that doesn't help then you may need thyroid hormone replacement. Hopefully the reduction in carbimazole does the trick. There can sometimes be a slightly delayed response to a reduction.
ok. From your previous results your current t4 look to be on the low side. Your doctor is wise to reduce your carbimazole and may need to stop it altogether. Too much carbimazole means that your thyroid doesn't produce enough thyroid hormone and this means that your TSH rises to try and get it to produce more. This should come down when the carbimazole is lowered enough to raise your t4 level.
I hope you and your doctor manage to get it under control soon. It must be very frustrating to feel poorly and not know when things are going to get better.
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