My first attempt at making a Fakemon... It didn't turn out as well as I hoped, but at least I got to practise some shading. :P
Any hints/tips on the shading, or the eyes? I'm not too happy with those either. :disappoin
Eyes usually don't have the same color outline the entire way around. Typically some of them will be darker shades of whatever color the face is. Look at how they are on this sprite:

You have some dark pink outlines around the eye which don't stand out a lot, but enough to give the eye a shape.
With the inside of the eye you have the white area, but the rest isn't just one color. Actually, it is one color, but it's usually more than one shade of color. If you look closely Mew has a few pixels that are light blue and a few which are dark blue. Peeky is right about the single pixel. That gives the eye a reflective quality which makes the eye look, well, like an eye and not like a flat design on the face.
As for shading, your sprite isn't very detailed. That is, it's round and smooth. Use a round, smooth sprite for reference, like my friend Wobbuffet:

Notice how the change in lighting is round, very round, rather than straight. Even though the light source is supposed to come from the left, with round objects it can look like it's more center/left and still be fine usually. This sprite is also a good reference for a general way of coloring the outline with darker lines toward the bottom/right and lighter ones toward the top/left.