T doesn't work any miracles. There are some doctors who actually think T might prevent more growth. NOt sure if this is true. But you are have a short sized family, so genetics are more important than T will ever be. There are normal sized people prescribed growth hormones. It's possible with a consent from the family (there are risks) and a very sympathetic doctor. It's still possible for you to grow a bit more.
Being a short guy might be a little of a pain, I am 5'1" so I know! But it's not the end of the earth as we know it. Actually I think I maybe care more than anybody else. Nobody really gives me a side long glance. I am read as male about 95% of the time but I don't think the 5% is due to my size and I haven't been on T a year yet.
--Jay