There are different types of PDA. Putting his arm around you or even holding your hand are the small types of PDA. Bigger types would be kissing in public, making out in public, or getting it in.. which is very provocative so be careful with that..
talk to him man to man and say "hey i know you're afraid, but every relationship goes through something like this and its normal. Nobody is going to care if you put your arm around me." then tell him how you feel.. like "I would be so happy if you put your arm around me because it lets other people know that i'm only yours and you're only mine".
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