(This will be long and I will be very direct. Apolgies ahead if I sound rude.)

Firstly, even if you don't have Photoshop, your scanner software sould let you select what is and isn't scanned on the image. There's a lot of unnecessary white space here that detracts from your image.

There are also free editing programs to be found online until you have aquired Photoshop or another, similar program. In fact, according to your last image, you do have Microsoft Paint, and unless I've forgotten everything about Paint it should allow you to crop images.

Don't be afraid to bear down with your colored pencils. Be they cheap ones, or professional quality, don't be scared of them. Work on making your coloring more even and more bold. Not necessarly bright, especially not if it would conflict with the image.

Part of what's making this image seem so washed out might be all the white space, but another part could be the water you said you used. Unless you're using watercolor paper, what's going to happen is you'll get really bad dips in the paper. Regular colored pencils don't react well to water either, and there are watercolor colored pencils. Your attempt at a "flowing" effect would have worked better with watercolor pencils. There are blending pencils avaliable for regular colored pencils, but a white pencil can work just as well, and actually might have in this case.

Since you are woking with a more anime-ish style (especially with this being fan art-ish), I would sugggest inking your lines before coloring. The colors here are very washed out, as I have said, and another reason for that is the lack of defining lines. Inking doesn't have to be done with an expensive pen, and there have been times I've just used a cheap Bic pen.

One last thing, and this will make your images really "pop": shading. It's difficult at first, but learning how to shade will really add a whole 'nother level to your work. For starters, it doesn't have to be detailed. Just simple shading at first.

You are a young artist, and one that has potential, but, like every artist, you have weak points. Knowing what the weak points are and how to correct them is the first step to bettering your art.

There is also one very important step in art that many people over look: take your time. A rushed piece won't look as good as one that took hours to complete.