His TSH is 2.6. What was your Dad's levels when his hair loss was occurring? I'm guessing 4x higher.
I don't disagree a more complete blood work with full thyroid panel (TSH, Free T3, Free T4, Reverse T3, Anti-TPO), would be helpful, but with TSH at 2.6 its not likely the issue.
And I agree - TT at 468 is not ideal at age 33, but it does not explain his hair loss. And Free testosterone is high so he has very functional levels of bioavailable testosterone - again not explaining his current symptoms.