I think the government will provide you with the injections if you are suffering from growth hormone deficiency (need to go through periods of blood tests...I think 2 days in hospital + a couple of times). The shots need to be taken daily, so you will have to learn how to inject yourself.
If you see a private doctor, you have to pay yourself. The shot for a 10 kg child is like 100 per day, and goes up with weight, so probably closer to 200 per day...And I think for it to have a lasting effect, you need to go for shots for 2 years...(probably cost of whole treatment HK$150k)