Hello and welcome Gray
Since you mentioned that you were having trouble with the eyes specifically, I'll focus on those. It's good that you added highlights to the eyes, they help to dispel the sense of flatness that comes from painting on a 2d surface you might also want to use some light greys for shading in the eye to make it look rounder. It might seem counter-intuitive to add grey to the white of an eye, but I think you will find that it helps a great deal when all is said and done. Reserve the whitest white for highlights like what you have in the iris / pupil already. everything else should be a little darker, and should gradually darken as you move towards the edges. It's tough to explain. I might try posting an example for you later. Basically, add value almost like you would if you were painting a white ball, but remember to reserve the whitest whites for the highlights.
Hope that helps! Honestly, I'm stunned by what you have been able to do without a tablet xD
"If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away."
-- Henry David Thoreau