I'm new to blender and trying to model a character, but I still don't have a full understanding of UV maps and texturing yet. He's got quite a few parts, so I was doing my best to fit everything onto the one UV map, but I decided to separate a couple of parts of him - namely his ears and wings - so that I could texture those separately, without having to fit them onto the main UV map. Here's my workspace.
I've done extensive googling but still can't figure out the answer to my question - Can I actually have separate textures/UV maps for separate objects? To be clear as possible, I have most of his mesh in an object called HeadBody. I put his ears and wings into another object called EarsWings. I want to texture each separately, but every way that I try to, even when adding a new UV map, it just ends up on the same crowded UV map again when I go into Texture Paint mode. I read a few things about assigning different Materials, but I couldn't figure out how to assign a texture to those Materials. Any enlightenment is super appreciated. Thank you!