My baby has a sty on her eye and its turning purple is this normal, she has had it for several weeks?

See your Peds. Your family doctor, pediatrician or an ophthalmologist should be able to evaluate and treat this. Don't hesitate, for your baby's sake. Good luck.
Examine. I'd recommend that you see a pediatric eye md to assess your child. These sort of bumps on the eyelids can be tender and if a procedure is necessary, then this type of md is very appropriate. Of course a conservative approach may be all that is necessary.