Your pituitary gland isn’t the problem and am surprised your doctors said so, your liver is producing too much SHBG and it scavenging too much of your testosterone. We are dealing with the NHS so misdiagnosing is expected as few doctors inside the NHS are knowledgeable enough. The NHS is the last place one should look for hormone therapy.
TSH is starting to indicate your thyroid is struggling a little, healthy young men see TSH closer to 1.0, . Reverse T3 might help explain elevated TSH, NHS will refuse this test do to costs. You can order it privately, suggest you go a private clinic. Men’s Health Clinic is Dorset, Dr Robert Stevens really knows what he’s doing. I think they do telemedicine, not sure though.
Hormone levels within the references ranges does not mean you are normal, however it makes it easier on the doctor since he can look at a number and determine you are normal for the fact that you are in the normal range regardless if your have symptoms. It gets you in and out of the office so the doctor can move onto the next patient, quick and minimal time is wasted and a the patient ends up without a proper diagnosis. This happened to you.
TRT results will depend on thyroid status which you can evaluate by checking oral morning and afternoon body temperatures using a glass thermometer. You want to see waking 97.8 and by 2p.m 98.6, if lower could indicate high Reverse T3 which can block good Free T3 levels. Reverse T3 needs to be less than 15 ng/dL, any higher and it could be blocking Free T3.
You won’t find anyone here on T-Gels, injectable testosterone is 100% absorbed so no need to worry about absorption issues and sweating off the T-Gel and contact with children. Those who have thyroid problems will fail to absorb T-Gels, pellets are problematic and inconsistent.