I had the "scratchiness" from about week 2, and the initial drop around 1 month. That said, I had a fairly low voice to begin with. As I recall, it dropped at month 1, month 3, and then sporadically from there on out. I've been on T about 3 years now, and I still have minor drops, but where it is right now is roughly where it's been for 2 years. I was 25 when I started; I know sometimes it takes a bit longer the older you are. Of course, it also depends in large part on genetics. You may want to talk to your male relatives... did their voices change early or late, all at once or gradually, etc.?
All I can say is, don't give up hope. I was a tenor after about 6 months on T, and now I'm a bass. It just takes time.
SD