Can recommend
Krita, it's free and excellent for drawing (less so for editing, but that's what Gimp is for).
NOW FOR THE DRAWING. Adding on to what Chaos said:
1. That shine isn't really working. You gotta remember to consider all the elements that it's passing over, right now it gives no sense of depth or roundness. Also, remember that hair is a fuckton of little strands, so having a completely flat border around the shine doesn't give the right texture.
2. What is... Going on here? I'm assuming it's some sort of shadow, but unlike all the other shadows, it's COMPLETELY BLACK. Unless you're going for a deliberate and highly stylized look with pitch black shadows, this is often a no-no. It's often worth picking two shadow colours, one darker than the other, so you can emphasize the really dark areas better.
3. You kinda swapped the arm thickness around here. The foreground arm is in full view, and as such, should be the widest visually. The other one is partially obscured by the chest, and therefore should appear more narrow.
4. This is probably just me being a nitpicker, but remember that even anime girls have white in their eyes. Also, eyes aren't rectangular, not even anime eyes. They may often narrow down to triangles and such, but when fully open, they're usually some sort of round, oval or almond shape.
5. I know that pretty little noses are the vogue amongst many, but there is still more to them than that. It's fine that not everyone draws great big ogre honkers like i do, just remember to hint a little bit more than just the side of the tip.
Just extending the curve a little is enough.
6. A lil' slip there, hee hee.
I'm not even gonna bother with facial proportions, that all falls apart when things get cartoony. Just remember, it's a good idea to know how to draw realistically so you can intentionally violate it. :v