Drills can be found in a lot of places--try either building stores (like Home Depot) or giant all purpose stores (like Target). You probably actually want a dremel tool, which is basically a smallish drill (at least, that's the impression I get). However, if you don't want to get a drill, you can try screwing in the eye screws before the resin has completely cured (as mentioned earlier).
I get resin on my hands more often than I'd like to admit, and I just try to get it off as soon as possible. I should really wear gloves.