You are a Michigan resident (and I assume your case involves Michigan doctors) so the first thing you should do is familiarize yourself with the Michigan statute of limitations. I am a Florida lawyer so I cannot give you specific advice on Michigan law but I can comment on general legal principles applicable to malpractice cases. You should, of course, consult directly with a Michigan attorney for specific guidance.
Use of growth hormones to increase the height of children is somewhat controversial in the medical field because there can be negative side effects associated with the use of these drugs. You do not say how short your son is or how old he is so it is more difficult to comment on whether hormones were an appropriate treatment. How long ago the doctor recommended no hormone treatment also may impact the statute of limitations. Are there any other physical problems your son is having other than being shorter than average? Certain physical conditions can make use of hormones contraindicated.
My best advice is for you to see an endocrinologist with your son. Often it is advisable to get a consultation outside of your local area because local doctors are frequently hesitant to be critical of other local doctors. A physician associated with a university medical school or associated teaching hospital may be a good choice. Ask his/her advice on current treatment options, whether earlier hormone treatment would have been advisable, and whether such treatment would likely have had an impact on your son's rate of growth. If those responses are favorable, you should immediately seek a consultation with an experienced Michigan malpractice attorney.