I know you want the best for your kid, but I can already tell you have a bigger issue with your height than he does just based on your "I'm 5'4, 5'5" on a good day".
HGH is unlikely to make him taller, it's going to promote muscle development that will require his body to intake even more nutrients to support the added muscle. Couple that with potential liver issues with long term HGH use, and you're on the road to early liver failure.
Feed him good nutritious food, give him a complete daily multivitamin for someone his age, and let nature take over the rest. Don't pump him full of steroids and other enhancers because you're insecure about your height.