Hi, Mio0
Hormones are not really that hard to get in Japan. If you're going to be in Tokyo, you could try e.g. MY Clinic in Kabukicho. I can't provide a link because of the forum terms of service (I haven't made enough posts) but if you google
myクリニック歌舞伎町
the site should be the first hit. There are many others, but this one has a pretty good reputation and is very understanding. (They have a very diverse clientele.)
The Saitama medical university among others has a dedicated gender clinic, and many private obstetricians/gynecologists can also assist if you explain your situation and ask for help.
As for bringing hormones with you, since they are for your personal use and not forbidden it should not really be a problem. The official import limit for any regular (non-prohibited) medicine is a two-month supply. Just be prepared to explain if you happen to be searched and asked what they are for. I've never heard of anyone actually being asked to show prescriptions or dosages, but that may of course be possible if something about the situation looks suspicious.
If you have anything shipped you may or may not get a postcard from customs asking you to clarify what it is and whether you have a prescription. That happened to me once, and when I called the number given they were satisfied with just an explanation on the phone. I've heard they may be a bit more strict these days—but I also know people do order from overseas.
Since you're already under a doctor's supervision at home, though, I'd suggest the easiest thing to do is to bring what you will and, should you run out, have what you need prescribed here—rather than pay for shipping and worry about whether the package will reach you.
I hope this is of some help.