You're probably fine (though it's the "probably" that always comes back to haunt you). That's about what I carry (plus a multi-tool I've never used) on my 24-mile commute.
Actually, with a patch kit and spare tube, you'll be good for about seven flats (put in the spare tube after the first, then when it goes flat you have half a dozen patches). That's really unlikely. Although, just to cheer you up, I once had NINE flats on an 11-mile ride. I ran over a thorny branch and got four, then didn't get all the little pieces out of the tube and had three more, then hit some broken glass. I walked to a pay phone and called somebody to come get me.