NAH - Gay teen bloke here. Your son came out to you because he feels ready to. I did the same with my mum and I didn't come out to my dad for a while. My boyfriend came out to his dad first and waited before being comfortable enough to come out to his dad.

It's a sensitive subject and with there still being such a stigma despite the year we live in, we come out to those we are comfortable with in the hopes they'll support us. Who we choose to come out to, especially in the early days, is a very personal thing. He'll come out to his father when he's ready. All you need to do is support your son and perhaps gently remind him that his father will also support him (that is, unless his father has homophobic tendencies and won't support him)

Absolutely do not out him to others. It's his decision to make.