Is there such a thing as wall lights that you can plug into a power outlet?
Yes, absolutely: what you want are called "wall mount plug-in lamps". You have a number of choices, e.g.:

See that pipe going downward? It's a conduit that dresses up the extension cord and protects it from getting yanked on. At the bottom is a standard plug.

These come in all sorts of shapes and sizes. I have one in my house which takes a 3-way bulb (50/100/150W) so you can get a lot of light out of them, and they often have hinges to let you swing them in and out.

Generally you will need to drill 2 holes into your drywall, hammer in a set of drywall anchors, and then attach a plate to it. (All the parts are included in the light.)

If you're renting, check with your landlord before drilling holes in the wall--but often it's easy enough to use spackle or compound to fill the holes you made, and then paint over it.