Testosterone can be administered parenterally , but it has more irregular prolonged absorption time and greater activity in muscle in enanthate , undecanoate , or cypionate ester form. These derivatives are hydrolyzed to release free testosterone at the site of injection; absorption rate (and thus injection schedule) varies among different esters, but medical injections are normally done anywhere between semi-weekly to once every 12 weeks. A more frequent schedule may be desirable in order to maintain a more constant level of hormone in the system.  Injectable steroids are typically administered into the muscle, not into the vein, to avoid sudden changes in the amount of the drug in the bloodstream. In addition, because estered testosterone is dissolved in oil, intravenous injection has the potential to cause a dangerous embolism (clot) in the bloodstream.
If a young man's low testosterone is a problem for a couple trying to get pregnant , gonadotropin injections may be an option in some cases. These are hormones that signal the body to produce more testosterone. This may increase the sperm count. Hedges also describes implantable testosterone pellets, a relatively new form of treatment in which several pellets are placed under the skin of the buttocks, where they release testosterone over the course of about three to four months. Injections and nasal gels may be other options for some men.
I think this approach is fine. I must say having been doing this for years, treating hundreds and thousands of men I have been underwhelmed with the results with topicals. Injections can cause peaks and valley and I have many younger men inject twice a week that smooths out the peaks and valleys. I think it is appropriate to follow the advice of your primary doctor and endocrinologist. I have just seen too many men spend months or years with gels with sub optimal results. Many men are diagnosed with depression and are not really depressed (I have no idea if this applies to you), but the presumed depression is base dupon low T.
My recommendation would be to pursue this but if a few months pass and results are modest consider another approach. Pellets are one approach to have smooth levels of T and are placed every 4 months.