PS is capable of true vectors in the form of shape layers. This is different from vexels and rasters. It's obviously not as versatile as Illustrator, but the basic capability is there.

The art isn't bad for a first but it looks a bit bland. Some shadows and highlights could probably improve it. They don't have to be overly complex, but simple one or two level shading can make a big difference. You could do a more interesting crop too -- dead center is often boring.