I doubt you'll get growth hormones, I've never heard of anyone getting them. That's not to say that it's never happened, but it's not something I've ever come across.
I think working through your insecurities about your height is the best thing that you can do at this time, maybe before even trying to get on T as it sounds to me like you're not sure if you'd want the T if you were to stay at your current height. It's hard to come to terms with, at 5'2" I'm shorter than even most girls I know, and have a struggle every time my work issues uniform or PPE. It took me 4 months, and into winter, before they could source a coat for me. I hate it, it's embarrassing, and it makes me dysphoric but it's a fact of life. I could have been this height if I was born cis. There's an instructor at my work, in his fifties, that is the same height as me (I reckon he's actually half an inch shorter but he won't admit it). Every time we see each other we make short related jokes, and this is how I deal with it. My height irritates and bothers me no end, but it's always something I can make a joke out of, and if I joke about it first then no one else can use it against me in a nasty way.