Buick Century 2002

Hi. I own a 2002 Buick Century. My low coolant light came on a few days ago but the temperature remained fine. All of a sudden yesterday my car temperature went way up and my car overheated. I pulled over immediately and the radiator reservoir was full of brown sludge. I added a little water after the temp went down and then 5 more miles down the road it overheated again. I left the car overnight and bought coolant today and put it directly into the radiator, but 10 minutes after driving it the car started to overheat again and white steam was pouring out as soon as I stopped. Any ideas what’s wrong?