Well, without LH and FSH your doc would have no clue what the root cause of your low T is. They're indicators of pituitary function. LH & FSH both signal your testicals to produce testosterone (LH) and sperm (FSH.) So, if your LH/FSH levels are low then your T is low which is considered secondary hypogonadism. Many things can cause this such as hypothyroidism, cortisol, prolactin issues, trauma, etc. If your LH/FSH levels are elevated and your T is low then the issue lies with your testicals not responding properly (primary hypogonadism.) There can also be combination of both.
All the above being said, many doc's simply don't know hormones as they are not trained in them in med school. It sounds as if he's just putting a band aid on the issue with testosterone being the "quick fix." Know that initiating TRT shuts down what production you currently have, it does not add to it. In most cases a competent doctor should be able to determine where the issue lies and attempt to address it. And you should want to know this, especially at your age as it's very doubtful it's idiopathic. I would hate to be on TRT at your age due to an improper diagnosis.
With what you've mentioned so far I don't think I'd accept another injection and I'd find a more knowledgeable doctor asap. Just the fact that he did not test LH and FSH send up major red flags. Plus the ridiculous amount of adex doesn't help his case. Take a look in the Finding A Doc sticky thread at the top of this forum and try to use the first set of BW there. You can pare down some of the items recently pulled without worries.
Watch this entire video. It's a great explanation of how our HPTA works:
https://www.youtube.com/watch?v=_xrU7HREfcU