OK, I am also "young" and am on testosterone. I was/am (I won't be getting any more doses but the last one is still in my system) on puberty blockers however, unfortunately, I did not get them soon enough to prevent or minimize things like breast growth and wide hips. This is actually pretty hard to explain without knowing your age, but I'm sure I'll manage.
If you are 16 or 17 your growth plates are most likely fused (or, close to it). If they are not (if you are still noticing vertical growth when measured, don't rely on relatives/friend saying you are taller for this because they will say that regardless of whether you have grown quite a lot of the time) the best thing to do would be to continue as I will explain for a 14 or 15 year old. The only way to know for sure is medical tests which will be quite expensive if you are in the USA. Basically, in this age group you can just start testosterone as normal and should not expect any bone growth (or very minimal bone growth).
If you are 14 or 15 then there is good news and bad news. The good news is your growth plates are most likely not fused and you can take steps to make sure remaining bone growth is masculine. What you need to do is get on puberty blockers as soon as possible. The downside is these puberty blockers are very expensive. Like, staggeringly expensive. The great news is on the blockers and nothing else you will continue to get taller the same way as a pre-pubescent child would. Most doctors will start your testosterone therapy at 16, but this is for consent reasons not medical reasons. When you start testosterone from the blockers you should start on a very low dose and over the course of 2 years (longer if you are younger than 16 and are allowed to start T) or so work your way up to an adult dose. This will very closely replicate male puberty and cause the maximum amount of male bone growth for your body.
If you are 13 or younger you shouldn't even be thinking about T. If you can get on puberty blockers at this stage you can prevent much of the damage female puberty will do to you. Discussions about testosterone will happen later for you but it is safe to say you will develop in pretty much the same way as any other boy going through puberty (although some things may happen a bit later if you have to wait until you are 16 for T).
Good luck man, it can be tough trying to transition under 18 but it looks like you are off to a good start. Keep your head up, the things you want will happen in time.