I agree USE A CRATE! Even putting him in a confined area of a room will not work at this time. Be sure to give him plenty of toys to chew up.

Put him in the crate while you are home anytime you are not actively handling him. Take him out often and love on him and put him back. Be sure he has water (you might need to hang a dog canteen, if he's apt to knock over a bowl.) Make sure he has plenty of room to stand up and move about in the crate.

Until he gets over his anxiety of you leaving, (which is a matter you might have to have a trainer to help with, should it be an issue) and gets over the need to chew (puppy teeth hurt coming in!) ...he needs to be crated.

It will make everyone's life easier (including puppy's ).