It sounds to me like she is interested in you...and just wants to string you along until she settles things with her old boyfriend. She might be acting so possessive of you in public because she wants to send the message to other females that you are her possession. I've seen women do this before...very catty. I would just make some comment to her in public that she should "keep her fork to herself"...or some half-joking way of letting her and others know that you are not her possession. Be nice about it, but be firm.