This sounds good so far. Stick with the Drs plan.
More t is not better with trt. You need enough to be in good range and feel good. If you go over range you will screw stuff up and require other meds to deal with symptoms, blood donation, etc
After about 6-8 weeks see how you feel. You will be feeling different things in the next couple of weeks or so. But you need to give your body a change to adapt.
You need to advocate for labs after this period. If Dr does not want to do them just tell him I would like them to be sure.
It would have been nice to get this before you started but that’s ok
Total t
Free t
Estradiol
Thyroid panel
Prolactin
Dhea s
CBC
Lipid panel
Metabolic panel
Shbg
Ferritin
If you are over weight I would get
A1c
Fasting insulin
Also you can learn by reading this.