I need some guy help

How do I get over my shyness in public. My boyfriend is so affectionate with me in private & public, & I want to be affectionate back but at the same time I’m scared. My dad knows basically everyone in our city, like everyone, & he is super strict about me dating so that alone makes me nervous to do stuff in public & the 2nd issue is I’m just plan shy. He says my shyness is cute but i still want to be able to reciprocate the affection. How do I stop being shy??