Hello Dreamof180,
With growth Hormone replacement, you still have chance at your age to grow. According to CDC in the USA, the average growth of men between 17.9 years and 19.9 years is 0.7 cm on average, but it some cases, growth can be much more (possibility to grow f.e. 5 cm and more, specially if puberty is delayed). Personally, my growth between 18 and 20 was approximately 2 cm. In some cases, there is even little growth after 20 (if growth plates are not fused and there is high amount of Growth Hormone/IGF 1)
If there is a fight with insurance, it is often benefitial to have a medical expertise/survey from a doctor (specialist) that the injections are medically indicated. I would recommend to try to get this from a doctor; than you have good arguments concerning insurance.
Greetings Morpheus