Why do I get shy around people in the public? But I am fine with my normal friends?

It's one of the traits of introversion: "More sociable and gregarious around people they know well".
Personally, for interacting with strangers it's a mix of difficulty finding the right words to explain why without any prior notice, and fear of awkwardness; with people in public, it alters the dynamic of interaction, since being within earshot one would refrain from certain statements.