Having your blood test in the afternoon will mean your TSH result will be lower than an early morning test and most doctors only look at the TSH result alone before deciding what to do.
The recommendation on the forum is all tests for thyroid hormones to be at the very earliest possible, fasting (you can drink water) and allow a gap of 24 hours between last dose of levo and the test and take it afterwards.
If I were you I'd try to get an early a.m. blood test which will benefit you best.
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