How do you get baby oil out of hair?

After using a combination of conditioner, hand sanitizer, and baby oil, I finally got a big hunk of silly putty out of my daughter's hair. Now I can't get the baby oil out of her hair! When I tried washing it, the shampoo wouldn't lather on her hair at all! I think it's because of the waxy build-up of the silly putty. How can I get that baby oil out?