Can I poly over the sides and that fix it NO

You NEVER paint the inside or sides of a drawer box. It's already coated and never ever needs paint.

Are they drawers on a drawer guide or wood rails?

Just sand it off and move on.

That's what I figured! He was a nut job! They are not on drawer guide just plain wood... I bought some of this tape stuff for drawers like these that are suppose to help them glide smooth but I was thinking it wouldn't help

Don't apply anything to the paint. The paint will release and you'll have a bigger mess.

First, I am sorry that you had such a bad experience with your painter! Sometimes hiring a painting professional can be a difficult task. For future reference, you might find an article we published a couple of years ago helpful: Choosing an Interior Painting Contractor.

In regard to your current dilemma, it's very difficult to give you sound advice without having some more information. For example, what type of surface was painted (pre-finished cabinets, stained cabinets, previously painted cabinets, etc.), and what condition were the cabinets in before? If the cabinets were not opening and closing without friction before being painted, I may have recommended readjusting them before painting.

Polyurethane will not help your situation. I believe the solution would be to adjust the cabinets, resand, prime and paint. There needs to be appropriate sanding and preparation of the existing cabinets, proper dry time and light sanding between coats, an appropriate primer which will adhere to the surface, and the finish coat should not be applied too thickly.

I hope this helps, and I wish you luck with your project! Please let me know if you have any other questions.