Do you have to sand and prime satin latex paint to paint over with an eggshell latex paint or can you just paint it?

Yes, Eggshell and Satin are very similar. Though i would recommend scuffing the walls with a sanding block or sandpaper to help with adhesion . Also current and new colors will make a difference, you may need to use primer if applying a lighter color over a darker one or if there are excessive stains on the walls.