I think the palette's fine. But your using a lot of
pillow shading.
Here I did a quick edit. It's not a great edit. It's just to show you what you did wrong. I changed the highlights and shadows to contour to the shape of the character.
I can't really put it in words so well. But look at his pants and hair as an example of what I'm talking about.
Also, your palette was a bit messy. I know you tried to only use the colors above his head, but you actually used 32 colors, some of them appearing only once.
Try to work on yours again. I didn't work very hard on the edit because I have to go somewhere soon. So I know you could do better than me if you tried harder.