There has been a clear connection between suboptimal thyroid function and low T in men for a very long time.
As you have seen increased TSH when starting selenium/iodine is a clear sign things were not optimal as the increase in TSH signals NIS symporter creation.
So regardless of where your labs were for thyroid tests means little. After all the lab range is not individualized but group biased. The only lab numbers that matter are your own historical numbers otherwise the labs really just show if your problem is severe.
Your T production may naturally increase on its own once you get thyroid in line. This can take some time (ie think 1-2 years).
Im all for hormones if they are needed. If low T is affecting you then by all means use it.
The thing to remember, regardless of the hormone, is that the body has many feedback mechanisms so introducing external hormones WILL prevent the body from producing its own. In the case of testosterone that means your body will not produce its own, additionally the precursor hormones LH (leutenizing hormone) and FSH (follicle stimulating hormone) will also be suppressed since they are what triggers test production.
So if you find you need to replace your T now until thyroid is up to speed sooner or later you will have to stop taking the external testosterone before you will ever know if your bodies testosterone release has been restored and it could take many weeks or months for your body to recovery and start producing ample amounts of testosterone again.
Im not saying to do it or not do it, hormones can bring about a lot of relief, just realize that sooner or later you will have to pay the piper and suffer with reduced testosterone levels for some time if you ever want to find out if your body has recovered. Otherwise testosterone replacement will be life long.