T.A.
S.,
Yes, you can still get chicken pox even after you've been vaccinated. I have seen quite a few kids in my childrens school come down with them, even after the shot!
However have you considered the possibility that they could be mosquito bites? The mosquitoes around here are thick right now, every time we are outside it seems we are under attack by them. I was looking at my 5 year olds neck which was covered with little red bumps and wondering what in the world it was, until I remembered the mosquitos. Just a thought.