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 is significantly correlated with aggression and competitive behaviour and is directly facilitated by the latter. There are two theories on the role of testosterone in aggression and competition.  The first one is the challenge hypothesis which states that testosterone would increase during puberty thus facilitating reproductive and competitive behaviour which would include aggression.  Thus it is the challenge of competition among males of the species that facilitates aggression and violence.  Studies conducted have found direct correlation between testosterone and dominance especially among the most violent criminals in prison who had the highest testosterone levels.  The same research also found fathers (those outside competitive environments) had the lowest testosterone levels compared to other males.