My boyfriend might be embared?

Okay, well my boyfriend (I'll use "m" as his name) is shy but just around girls. And he's soo sweet around me but at school he's a real trouble maker, but he won't hold my hand becuz he thinks we'll get pda. When we aren't at school M holds my hand, walks with me kisses me and is very protective, even around are friends. Is he embared? He also won't kiss me anymore then a peck, nothing long ever and he's never really kissed me, I'm not sure if M is embarred. Please HELP