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.
Physicians and those in the mental health fields suddenly noticed that a substantial percentage of depressed men were low T and giving them testosterone helped very often. The subject of Testosterone and Depression is so important that I did a page on it and documented the many kind of depression and mood conditions that HRT can help with. In my opinion, if a man is struggling with depression, one of the first numbers that should be pulled is testosterone.