Hi! Great character, the expression is well done. I did an edit to show how you might shade the hair to achieve a satisfactory result. Here it is:

First and foremost, simplify and carefully edit your lines. Hair is heavy, and droops down after only a short distance, so curls and strands all wobble down simple vertical lines.
Another thing is to remember that you don't necessarily need to keep outlines inside the main image. The bangs do need a little shading to pop out from the forehead, but not much.
The next step is to color clumps of hair, in very simple shapes, editing out the outlines as you go. Hair reacts to light like lots of tiny silk ribbons--and you can make your work easier by pretending there are only a couple major ribbons to draw.
And then there's the major thing: consistent light sources! All the ribbons have to be lit according to where the light's coming from. The ones with most light will be brightest throughout. When you're drawing out the basic lighting for the hair, try doing clumps and ribbons in single colors, according to their brightness.
Finally, go over the hair and add more contrast to curls if you feel it necessary, adding details and tweaking colours. I edited the four hair colors as I did the larger edit, and tilted the shadows towards blue.
I really hope this helps you with your hair troubles. Good luck with your character!

Fantastic work! The hair is great, and the shirt is coming along just wonderfully.
The idea of tilting towards blue (or any color, for that matter) is a way of mixing in complementary colours, among other things. It actually is an accurate representation of daylight--the sun provides a lot of bright, warm-white highlights, whilst the sky casts a weaker blue light onto everything. Where the sun doesn't light an area, the sky does. So if the darker colours we draw with are tilted towards blue, it just feels more natural. It's how we're used to seeing things.
The complementary colours thing means (please don't quote me on this, I'm probably about to make a complete train wreck of colour theory) that if we have a warm colour, like red or pink, and put it next to a cool colour, like blue or teal, it creates interesting harmony. You had already done this with the shirt complementing the character's skin and hair, and it's a simple next step to do it inside the palette of the individual materials.
One final note (whew) on tilting colours to a certain colour is that if you do it just right, you can cut down on the amount of colours used. For example, you could use very small amounts of the dark purple from the hair, and the lightest green from the eyes, to AA the shirt. The skin could be edited so the darkest tone replaces the darkest part of the hair. It's trivial, but I for one find it very satisfying, and it connects all the different parts together.
And that's why it's neat to tilt colour ramps towards certain colours!