Low T with high LH/FSH means that your testes are not working aka primary hypogonadism.
Your FT will be low, do not need a lab to know that.
Did this happen suddenly or have you struggled for years.
Please read those stickies.
You should be self-injecting T, 50mg twice a week. Doc will have other ideas.
If you only inject T, your testes will probably shrink and you can easily become infertile. You need to have an explicit conversation with your doctor. 205iu hCG subq EOD or 20mg Nolvadex EOD will avoid those problems.
The E2 lab test does not resolve below 20pg/ml, you might ask if a more sensitive lab can be ordered. You will see that we suggest all almost all will need anastrozole to have optimal E2 levels, near E2=22pg/ml. Many doctors do not understand this at all. The male adult range is shown as 7-56 and 56 would be a disaster. If doc is bound to lab ranges you will need to try to find another doctor.
Have you had your testes examined?
So yes, you do need TRT, no known way out of your condition. - unless you had severe vascular abnormalities of both testes that were surgically repaired.