Yes, it is possible for lactose intolerance to develop at any age. I am in my mid-40s, and just started having trouble with it a few years ago. Up until then, as far as I know (!) I was okay. I have different symptoms than you do. For me, I just get bloating, gas, and cramping, but it's still unpleasant. So I avoid milk and dairy products, and I find I feel much better.

Take care,
ErinBear