Maybe it's just me, but when I ride hard (or mash gears or do a lot of hills or try to keep up with the fast group), my quads hurt! As long as it's the good kind of hurt, vs. pain from an injury, I think you're okay. Give them a good stretch afterward and use a foam roller or massage stick to loosen them up.

I would also play around with your position on the saddle. When you're pedaling in the drops or on the hoods, you tend to use your quads the most. Slide back on the saddle when you climb to engage your glutes/hams and to give your quads a break. Stand up and climb, slide to the nose of the saddle and see how that feels. Moving around will work the muscles more evenly and give your quads a break.