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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.
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.