This is cute. Your style adapts well to pixel art. Background elements remind me a lot of a comic book style. I'm not talented enough to know what issues you describe with the hair and neck but I think it looks fine. Maybe the chin outline is a little thick or something? Choice of colors for shading/etc is really really good. The dither pattern on the desk/floor is a nice touch too

Cute Drawing! >^< There's another her there!