Is My "girlfriend" embarrassed of me?

We've just started dating and everythings' been going great, but until recently that we ran into her friend on our date; she lied to her friend about me. She told her I was 23 yrs old, that she met me at work and that i work at a park. She never holds my hand in public and when we do, she slowly wiggles it away. I put my arm around her and she moves away. When i try to kiss her, all of a sudden shes worried about her surroundings. When i walk her to car, she waits for all her friends to leave. When we text or talk, shes all "lovey dovey" Any ideas or suggestions?