I was out at a club three days ago and was dancing with a lady that I met. After dancing, she gave me a few pecks on my right cheek and one on my left. Moments later, I noticed that she had a red dot on the edge of her lips that resembled a cold sore.

Ever since then, I have been freaking out about it... Are my risks of contracting herpes high in this situation? Or do I have a fighting chance?

First let me say that I don't think you will get from that instance.
Now I will say...
When a person has an active cold sore, they are definately contagious. Herpes (cold sores) "prefer" the softer tissue of the lips or genitals, but can appear on any place on the body.
I don't think you chances of getting it are anywhere near what they would be if you had kissed her on the mouth.
Good Luck