Can i go to the beach with a cold sore

Yes: Cold sores can be contagious in the beginning but after several days less so. Most infections are caused by direct contact.

Yes: Just rember that they can be transmissable. Cold sores can be spread by touching cold sores (for instance if person with cold sore touches it with their hand - the herpes simplex virus can be spread further from there), kissing, sharing glasses, silverwear, toothbrushes or other personal items.