At the risk of making generalizations, Japanese tend to have a strong sense of shame. It is possible that the shame is now haunting her; despite our progressive society, it is possible that she now feels guilty about dating you, possibly because she's your dad's student, or because she's worried about other people's approval of your relationship. This would explain her dislike about you two being touchy-feely in public.

I cannot offer any useful advice, I'm afraid. Perhaps you should confront her about it, but this could be dangerous, and even if she did open up to you, it will be very hard to erase something as ingrained as shame. For now, maybe it would be best to cut down on the PDAs until you've discussed things with her more. I wish you the best of luck no matter what you do.