Riding out into the sunset
By the sounds of it, she may be losing interest in you. I suspect her kindness in public is to just show you that she isn't mean or anything. I've had the same thing happen to me before.
I think your best bet is to just move on and give her the cold shoulder. If she does still care about you, she will notice and come for you, but don't try to pursue her. That just makes you look needy. If she does come back to you, then you can make the choice of whether to let her back into your life or not.
"There is no better than adversity. Every defeat, every heartbreak, every loss, contains its own seed, its own lesson on how to improve your performance the next time." - Malcolm X