The way you are shading right now is tempting to pixel art beginners because it looks smooth from a distance, but unfortunately it doesn't describe any meaningful lighting.
Especially when you are working with a character that has a main tone of black on the surrounding portions, becoming darker near the edges only serves to mystify those boundaries, as the softer the transition in tones is, the harder it is to not see the jump to black as a gradual one as well.
If I had color advice, it would be to lower the saturation of the main blue where the most light is, and only saturate that much in areas where light is bouncing around between blues, such as folds. In doing this, people usually end up with a more desaturated bright end of a palette and saturated dark end.
Another artifact of pillow shading as you have done is banding, which is where horizontal or vertical lines of pixels appear to hug the boundaries of other pixels. you can see this below the shirt or on the beak itself, where the steps in the lines serve to create rectangles out of the shading and work against the purpose of shading - that is, to describe a form.
