First most doctors are terrible at diagnosing low T, yours may have failed to run adequate labs!
Those are great numbers, but we see guys in here all the time with high SHBG, high TT and lower FT. Essentially if SHBG is high enough it will bind up all T and since FT is the active hormone it matters more than your TT number. I’ve seen guys with over 1000 ng/dL who feel terrible do to high SHBG which shrinks FT and just because you are within range doesn’t mean you are alright. I’m willing to bet your SHBG is high end of normal range.
Most doctors knowledge is limited and narrow within their field and the result is a doctor who stares at a bunch of lab numbers to make decision not realising everyone is different, SHBG is known to increase as you get older and it starts binding up your FT as you age. Your FT is low compared to your TT, was your FT labs direct measured or did you get it from through calculating SHBG, TT and albumin? This is how we obtain accurate FT numbers, any other method is good enough.
If direct measured these labs are inaccurate and your FT could be even lower. Post all labs including ranges. Thyroid labs are needed, lots of symptoms of a lagging thyroid has some of the same symptoms as low T.
You need more labs as yours are inadequate.
https://naturalbiohealth.com/2015/05/06/shbg-critical-to-your-health/