My daughter also has TS. We started her on growth hormone when she was 15 months old, so it has been just over three years. I am a big fan of growth hormone, which has been around for a long time and extensively studied. We have not experienced any side effects (though there are some - aching and headaches can be common when you start or adjust the dosage). The issue with growth hormone is not just one of aesthetics - it's not just that these girls with TS would be short - but that it helps with all kinds of healthy growth. It sounds really hard - so many years of daily shots - but it's actually quite easy after the second time you do it and my daughter, at 4, can give herself her own injections now.
TS can take a lot of management, but the outcome for girls who start growth hormone early and have appropriate interventions is quite good. If I can help you with anything, please feel free to send me a personal message (I don't really come to this forum very often - a friend forwarded your post onto me).