In this situation one suspects?
- high SHBG, get that tested
- TT is inflated by SHBG+T, overstating your T status
- FT is decreased by SHBG+T
- T production may be low. LH may be low or testes not working very well.
You can test LH/FSH to see that the signals are. Also check AST to eval liver. SHBG is made in the liver. List all medications of odd things about diet/supplements.
Your low E2 is not promoting high SHBG, but low T might be.