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

You stand your ground, mama. Don't buy him that toy because he's screaming. Just keep calm, tell him you don't appreciate his tantrum, and the two of you just walk away from the store. Explain to him he can have the toy under special circumstances: if mama can afford it, it's his birthday, he has earned it by doing chores, etc. Up to you what those circumstances are.