Hormone blockers will stop female puberty, assuming you haven't completed it yet (which it sounds like you haven't)
To my understanding, hormones are what stop growth, so blockers should help you grow taller if you're still growing. If you've stopped growing on the other hand, it's likely you wont grow more (but still possible). From your parents' heights I'd guess you've still got growth potential but I'm no doctor.
Testosterone when you're still growing is usually not recommended, however there are debates about whether it stops growth or not. As for the growth hormones, I have very little knowledge.
I think now you can start T almost whenever you want (but the younger you are under 18, the harder it is to find a doctor), however it is highly recommended that you talk to a gender therapist to make sure you are emotionally and mentally ready for T. When your doctor deems you ready, then they'll send you to an endo. With some guys, the therapist knows right away that they are ready, and with other guys, sometimes they need to straighten things out in their lives or think a little deeper about things first. It's not just a simple "you're ftm, go get T." Once you get to the endo, it can either be immediate or they may wait for blood results to come back before prescribing T.
I started puberty about that time I think, and sadly I'm still the 5'1" I reached when I was 12. Of course, everyone is different, so hopefully you'll keep growing to be 5'7" or 5'8"
