Can I get infected by getting cut with a razor blade..?

I am not cutting, promise. But, I needed something to use for my school project, so, I took apart a Gillette disposable razor. I found it in the bathroom cupboard with a bunch of others, probably my Mom's... while using it I got a small cut, nothing major, but there was blood. Afterwards I got a bit scared and washed the blade, and the cut? Then I put a band-aid on it. Could I get infected, or will it be okay--? And for future reference, are there possibilities of getting infected, if I got cut again, even though I washed it? Thanks. :) xoxo