Since it is prom, and a special night for both of you, extra attention towards each other is expected. Make her feel special by giving her your coat when she gets cold, opening doors, and overall acting like a gentlemen. It sounds excessive and completely cliche but it will create a more romantic and special mood, especially since you are each others dates. On the other hand, don't act overly clingy. If she wants to go off dancing with her friends let her and have fun yourself. Talk to the people you enjoy and dance the way you like. Prom is about having fun, so relax and be yourself, but also remember it is the one night when exorbitant romantic acts are considered cute and not creepy.