I primed and painted a steel door without sanding first, and now it feels sticky. How do I fix this?

I talked to the guy at the paint store and took his advice. I was told to prime and paint three coats, so that's what I did. However, after finishing and giving ample time for the door to dry, I heard a strange noise as I opened and closed the door, and it also felt sticky on the surface. I am wondering if a light sanding and then adding another coat of paint would do the trick? Can anybody help me? Thanks! Kathy :)