What should I do if my preschooler wouldn't stop screaming because I didn't want to buy him a toy at the mall?

Well, you're going to have to hear every screeching scream until he decides to stop. Your child is screaming because he discovered that it is an effective communication method when it comes to getting what he wants. The best thing you can do is to quickly let him understand that your preferred communication is not to have your eardrums suffer. First, don't mind him (so he understands that this "cause" has no "effect"). Second, give him tools to communicate anger/frustration with you. Maybe he can cry quietly in a corner or ramble of to let you know how displeased he is. Third, validate his feelings by saying, "I know you want the toy now, but...". Fourth, set expectations for next time. Before going to a mall, make him understand that you are there to buy him a lunch box and not a toy.