I find pixeling hair is kinda a trial and error thing, and wont necessarily look complete until it has some sort of harmony. My biggest advice is to think in terms of clusters. don't try to make strands of hair. You can't pixel strands of hair at this size since the pixel is too big.
Instead, think in terms of fat curls and waves. I prefer to start with the highlighted curls or waves. Once I get the shapes I like, I add in shadow areas. Then, I simply add little bits of detail here and there to break up the big patches of color. Pixel art is often about the little tricks and bits of ingenuity: Since I couldn't pixel strands, I thought I could suggest hair a little more by making the outline of the head a little wavy here and there on top, and I could go thinner with the waves with the darker color in the final stage of tweaking, since that color didn't stick out as much, making the lines actually appear smaller.
Also, it is said often to try to pixel on a grey or neutral background. Trying to work on a very bright or very dark or high chroma background can make it hard to select the right colors for your piece. You also had like 120 something colors? Not sure why that is
