Epstein-Barr is a red flag - it is not normal nor was your TSH. Yes keep looking for a better HC provider.
I'm not going to say you have a thyroid problem. But I would have your TSH, T4 and T3 tested again after your infection clears up. Infections, stress, and dieting can cause thyroid hormones to go low. But doubtless many people with thyroid issues feel badly long before their lab ranges go off clinically.
Hopefully it's the Epstein-Barr infection doing you wrong.
Your story is all too familiar... may people in the lower part of the ranges are determined to be "fine"...... Did anyone bother to suggest a cause for your fatigue? No? I didn't think so...... because they'd have to admit that it's thyroid.......
Just because you're not missing periods doesn't mean you don't have a hormonal issue......... wow, these doctors can really get "out there" can't they?
First off, your lab is using an outdated reference range for the TSH; "new" range, established nearly 10 yrs ago is 0.3-3.0; yours is clearly above that.
Second is your FT4; your level is 0.89 with a range of 0.82-1.77...... you are just barely in range there and I can almost bet that neither of your doctors even really looked at the FT4; they were zeroed in on the TSH.
I might suggest that you try to find a different doctor who will treat by symptoms, rather than completely relying on labs.