Can I ask how the plug worked before? Did it come on with the ceiling light? Was it always on?

Sorry if that's over explained. You need a white pigtail and hook the red straight to the gold screw. Make a hook on the end of the wire to go under the screw.

Two whites are neutrals going onto the silver screw. You'll need a third wire coming from the two whites to connect to the light socket. The red goes straight to the gold screw. It's the return wire from the black hots in that box go to the switch and come back on the red to turn it on. If you wanted the light to be on all the time you'd hook into the blacks.