I never properly grew out of it, but the symptoms did get less. I think I was about 10-12 when I started drinking milk again more often. I still didn't drink it very much, because if I had too much at once, i'd get a sore stomach, or ezcema.
This continued even until I was 15, but at that age I stopped drinking milk for animal rights reasons. The symptoms never completely went away, but they were not as bas as they were when I was 2-8 years old.
Hope this helps. Soya milk is definitely a good alternative though, and it's quite tasty.