relationships!

So I've been dating this boy for a month now and I like him a lot. But he's really shy in public and I try to flirt with him and talk with him but he's super awkward in public. He won't hold my hand or hug me or even touch me at all. I don't want full on pda with him but I want some affection from him in public. How do I get him to do that? How do I deal with his shyness in public?