Yeah, tire levers are the best way to get 'em off. I used a screwdriver the first time I changed my tires and ended up puncturing the tube, just like you. Once I got tire levers, I was able to trim the time for a tire change to about 5 minutes.

Don't get frustrated (and don't pinch your fingers; it hurts!); just go out to the LBS tomorrow and tell 'em you need a set of tire levers. Should be about $3. Good luck.