Sorry I can't help with info on any of the free editing sites, since I don't use them. Hopefully it is possible, and someone will Answer with that info.
If you know someone who has photoshop, they can easily correct that shadow. (They can Select the area and change the brightness.) If they have CS3 or CS4, and you shot the image(s) in RAW, it's even easier. They can add a Fill light, And correct the ambient lighting for you, too :) Shadows, as you noticed can dull the light in your eye, and cover up that energy.
If you have a photography/visual arts instructor at school, check with them.
Just a little bounced light would eliminate, or lessen as much as you want, that shadow. You can reflect light toward your face, by simply using a sheet of white paper, out of the image frame, to bounce light up onto your face.
With a 7.1mp camera, you probably have the option to shoot in RAW. BUT, all RAW photos MUST be processed in an image editor to be most effective. Don't shoot in RAW, unless you have the option for post-processing. I doubt if any of the free sites will allow you to process/correct RAW images. If you don't have an editing program, shoot as a large sized JPEG, to give the best possible image data for processing. Unfortunately, Large JPEGS will take up more room on your memory card, so keep an eye on that. And, any free sites may limit the JPEG size of the image you can upload.
Good luck :)