Question about screen printing ink - do I really need a screen?

So I want to do a project for my girlfriend, and was planning to just screen print an image onto a pillow case. I've looked through some tutorials, and it seems like since I'm only going to do it once, and the image would be kind of large (since it's for a pillowcase and not a T-shirt), could I just paint the image onto the case with screen printing ink? Do I really need to make the screen or stencil? Or would the ink be all dry and crusty like fabric paint if I did it that way? Or...yeah. Any help is appreciated.