My son is just 15 and at 3.4 according to your Tanner calculator.
I am in the military and am very concerned that he is very shy and modest almost like a girl. I haven't seen him naked since he was maybe 6 or 7 because he hides himself very effectively. From seeing him in underwear or bathing suit, his genitals appear to be in line with other kids of the same age and physical stature. We went to buy diving gear and he was told to strip naked to try wetsuits on and he flat refused, but it's impossible to don a wetsuit solo, so no diving for him. I'm concerned because he wants a military career, but the trauma of the communal showers and open displays will be a major shock to him. I've been brutally open and honest in how it will be, and he just shruggs it off. When I take him to the doctor it's a fight for the doctor to check for hernia and testicular cancer, he makes the doctor feel through his underwear and won't let him look.
Do I put my foot down and force it? Have him sedated, so he can be examined properly, or what? This irrational modesty is ridiculous in a maturing male. Help me understand my son's wierd behavior. They don't make the boys shower in school gym class anymore because mothers have complained about it, calling them dumb jocks and neanderthals. Mommy crying about her son being naked is making these boys into little crybaby pansies in my opinion. I honestly don't think he has ever seen another naked male, ever. He refuses to change to swim with the boy scout troup and opted out of the sex education discussion. He's a good boy a total pleasure to have, a good student, respectful, plays sports well. Just has this blantant refusal to act like every other 15 year old I know who strip at the drop of a hat to take a dip in the creek with their buddies, but not my son. It's almost embarrassing.
I believe you are overly concerned about a minor thing. Without him telling me what is going on, I would assume that he is just a very private person. There is nothing wrong with that. Yes, he is going to run into a problem if he decides to follow you into the military, but either he will resolve that issue by the time it becomes important or he will change his mind about his career field. In regards to exams by the doctor, leave that between him and his doctor. Just let him know that if he has any issues or odd signs appear that he should not let his discomfort stand in the way of seeking out help. If you don't make a big issue out of it, he will likely grow out of it.