I myself am not an artist who draws in the anime/manga style but I think that I can provide some opinion and guidance based on what I'm seeing in this work.
First I'd like to point out that you have given this work a good sense of proportion - the curve of the face is very well done and overall there's some real potential here once the rough edges are smoothed out.
You don't talk about how you created the work so I'm forced to guess that perhaps you drew in pencil and then inked over the original lines?
I'm guessing at that method because I'm seeing what I think is a "doubling" of some of the line work along with appears to be a number of 'hesitation' marks on the longer lines.
Either way I would suggest that you work on giving your line work a 'smoother' appearance by using longer, steadier strokes so that the lines look more fluid and less shaky. If you are tracing over pencil work with pen you might find it easier if you use the pencil more as a guide rather than trying to ink directly over it or you might be able to achieve a smoother line by using a different pen type since some just lend themselves to a fluid line better than others.
As you pointed out yourself, the characters left eye is a bit "off" when compared to the right eye so I won't dwell there other than to suggest that maybe providing a more solid coloring job to the eyelashes might have helped clean them up a bit; right now you can see the individual pen strokes and it's a bit distracting.
There is a similar issue with the hair. I think ideally you want to try to present the hair in this type of drawing as a solid color as much as possible. The individual pen stokes are visible here and while that alone is not necessarily a bad thing those strokes are going every which way and appear 'blocky" in that you scribbled them in every couple of inches rather than carrying through the line work along the length of the hair; this makes the hair look a bit stiff and clunky despite the wavy outline you've given it.
The hair also has some lighter areas spread across it. I'm uncertain as to whether this is a deliberate attempt at highlighting the hair or if it is an accidental result of bearing down on the paper while you filled in the color.
If it is a deliberate attempt at highlighting then I would suggest that you study how the more advanced artists draw this in; it's usually treated in what could be considered to be a more deliberate and stylized fashion then what you've done here with a bit more attention paid to where the hair should "shine".
If those lighter areas are the accidental result of putting uneven pressure on the paper itself then you can probably address that by changing drawing tools to something which will enable you to place darker color using less pressure.
I would also suggest that you experiment with giving the body of the hair a more flowing appearance with softer curves which would reduce the branchlike appearance - with smoother curves and a more flowing appearance combined with a more solid color the hair alone could give a piece like this a much more striking appearance and more impact.
The last thing I'll bring up is that I notice you've made some token attempts at shading along the shoulder and collar bone area along with under the chin. I'd suggest doing away with this shading entirely and try to focus more on a high contrast between very pale while skin and very dark flowing hair - if you get that going for you the token shading becomes entirely unnecessary and distracting.