Welcome!
A few suggestions from me:
- I guess you've saved this as a .jpg at some point, because you've got a crazy number of colours for such a small piece. Make sure you always save as .png or .gif, to avoid distortion and extra colours.
- I've reduced it to about 8-10 colours (I forget) just to show that you can get nearly the same results with less than 10% of the colors you've got right now. I recommend that you start with as few colors as possible, and add new colors sparingly. This isn't to imitate the color restrictions of old school games or anything, it's just to give you more control, making it easier to work with what you have. Mixing the balance between colours is like juggling, and the level of difficulty increases very rapidly as you start juggling more and more stuff.
- Didn't make a lot of changes to the character, but tried to clean up some lines, get rid of jaggies, work on the shading and moved the eyes a bit further down, while making the cranium a bit longer.