I will be flying domestically soon, on United Airlines. Can I carry on a blanket/pillow + laptop case+ tote?

That is a pretty big pillow and blanket to hang onto. Why not get a space bag and squash up the blanket and pillow in it. You can buy them at Walmart in the same aisle where clothes hangers are. Then it should fit in either your checked luggage or carry-on and be much smaller. They work great for clothes in your suitcase too.