1998 Chevy Blazer I need help with my car

My blazer had a small leak in the radiator for a few months.I kept topping it off with water and it overheated a few times. Finally the hole in the radiator expanded and the car lost all water and died out while driving.I replaced the radiator and starting the car was hard at first had to get a new battery but when it finally started water was shooting out of my tailpipe then it turned into thick white smoke. And I noticed it was antifreeze burning out from my radiator which was emptied within minutes of the car running. The smoke had stopped until I refilled the radiator with water. Then it started to smoke again from the tailpipe until all the water was gone from the radiator. What could this be and how much would it be to fix? Thank you for your time.