I hope you don't mind my two cents. I've been through army basic training. Now, the first part of what I'm about to say is going to sound insensitive and for the life of me, I don't mean it to be...but if your son is old enough to go through boot camp, he is old enough to hold his own and learn lessons if he can't; he doesn't need his mom talking to the drill sergeant for him. I'm sure he is justifiably mortified. Yet at the same time, keep this in mind...your son is YOUNG. He is not going to hold a grudge forever. As we grow older, go through things, and mature, our outlook on many things change. The drill sergeant was doing what a drill sergeant does...what he did does not surprise me in the slightest, but it was not necessarily a bad thing (although for a little while it may seem like it). He's going to make your son work hard so that he can succeed.
Boot camp is a life changing experience, and despite the fact that he may not be happy with you right now, I'm sure he will be so thrilled to have you attend his graduation. I've known of other, very troubled (I'm not saying in any way that your son is like this, okay?) young men who have completely blossomed in the military. He will be proud to share his accomplishment.
Speaking from personal experience, I was a bit rebellious in my later teens and had a few years I'm sure my parents would love to forget, but we have an excellent relationship now and I can truly appreciate what they did for me when I was younger.
Allow your son to stand on his own and be supportive of him. As someone else mentioned, do send things in plain envelopes LOL. I remember that we had to do 10 pushups for every letter we got...yet we loved getting those letters and packages (I forget how many we had to do for those!). Send him letters about what's going on at home. Don't feel bad if you don't get many letters in return...there is little time for letter writing, but know that each and every letter is appreciated. Let him know how proud you are of him.
I'm sorry this is so long, but it kind of struck a chord with me and I wanted to give you a perspective you may not have thought about previously. Things will get better, I promise. Don't let your son leave without telling him you love him and are proud of him. Let him process things on his own, in his own time and it will work out.
Okay, I just read it was the sergeant rather than the drill sergeant. Either way, I'm not surprised...that's kind of how they function. They'll work your son hard and he may not like it at the time, but it will enable him to succeed. Keep your chin up, okay?