Can I use an amateur radio for a science fair? If so, do I need to prove that I have an active license?
The short answer is probably. Since amateur radio is a scientific hobby, that would be a great science fair project.
You should check with the science fair administrators before you do a lot of preparation, but I cannot fathom why any science fair would reject an amateur radio exhibit. I suggest you make certain that you present your exhibit as scientific somehow, and not just present it as (for example) "Hey, I can talk to the local net, and that's fun", or present it only from the aspect that hams sometimes use it to provide a public service (like storm spotters, or disaster communications when no telephones are working).
In any case, bring a copy of your license. You can print it from the ULS page, I believe. My wife and I keep a copy of our FCC licenses with us at all times.