TRT is Testoterone Replacement Therapy. Obviously, it makes good sense when prescribed by an Endocrinologist for men with proved low testosterone levels. Women also have some normal level of this hormone, lower than in men.
I'm not quite clear about your wife's condition ; you mention low energy, sleepiness and irritability. There are many possible causes for such problems, potentially including Depression, though usually with other more typical symptoms of depression. You mention depression as a diagnosis : who made this diagnosis ? If it was a psychiatrist or a clinical psychologist, I'd expect this to be correct ; if made by another doctor, GP or specialist, I'd be less confident, and would prefer the view of a psychiatrist.
If indeed the diagnosis of depression has been correctly made, then there are many treatment available, including antidepressant drugs and CBT counselling, which research has shown to be effective, and which should be properly tried before one experiments with unorthodox methods which might or might not help.
I have seen some evidence, not yet conclusive, that there can be some improvement in symptoms of depression and cognitive problems, with the use of TRT IN MEN WITH established low testosterone levels. I notice there seem to be quite a few law suits going on in America, against drug companies, concerning problems allegedly caused by TRT
I don't see convincing evidence that it's useful beyond a placebo effect if these levels are OK. There have be few trials of TRT in depression in women, and from what has been done, I see no reason to believe it's a useful treatment for their depression.
Doctors who use unorthodox or still experimental treatments, should discus with their patients their reasons for doing so, possible risks and benefits, etc. So do discuss this with whoever is treating her.
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