Hmm. Do you get appointment summaries/paperwork after your appointments? I do, and it tells me about my diagnoses, current medications, etc. I've also heard of doctors emailing this stuff, or posting it to an online medical chart or something like that for the patient. If not, I'm pretty sure you can request a print-out.
But yeah, that's really weird. As for me, my doc started me on shots every two weeks, and a nurse taught me how to inject my own testosterone after I picked up my first prescription.
I specifically asked her about changing my injections to weekly because I noticed I was feeling "down" by the end of my two-week doses and I'd read that weekly injections can keep your levels from fluctuating as much between shots. She's new to treating trans patients but was very open to this and lowered my dose to let me switch over.
I'd suggest calling or emailing your doc (or request an appointment) to let them know that you'd like to talk about your medication and be counseled on exactly what it is, how it works, how it differs from similar types, etc. Also ask if they prescribe other forms or Testosterone that you can administer to yourself at home.
With many doctors, you have to be firm and persistent or they won't respond to you, unfortunately. Just ask for specifics and don't let them leave without clueing you in.