While your results might be within the normal range, they may be at the wrong end of the normal range for you. Think in terms of a grading system. Any grade from D- to A+ is passing but would you rather have a D- or an A+? If you're trying to get into grad school, getting an A+ is pretty important, than if you just wanted to graduate.
Another interesting paradigm is to consider that grades have no inherent value in and of themselves. It's the recepient who makes the grades important. For instance, while all grades from D- to A+ are passing, perhaps even a B+ is a relative failure for someone shooting for valedictorian and Dean's List w/straight A's. On the other hand, that very same B+ is a miracle to the person who's just trying to slide by.
My point is this. Just because your test results are normal doesn't mean they're optimal for you. You might ask your doc for a trial of branded levothyroxine. See how you feel 6wks later and don't forget to check your labs while on the medication.
Last point: you didn't really go into detail as to why you might have hypothyroidism besides having a low basal body temperature and feeling exhausted. Don't forget that other conditions can also rob you of your sense of wellbeing. Good luck!
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