My bmw 328i won't stop overheating

Yes the fan works but when the car gets hot its really loud. I did have an antifreeze leak and had to use water in a pinch to fill with cause I had no coolant. I might have left a bit in the cooling system when i drained it. Couldn't get under the car so i pulled off a hose ti drain the best i could. Would that make it overheat?

At first, all 328i from 2006 t0 2011 have a warranty up to 150000 miles on emission cooling system is part of that BMW dealer they would fix the car on there warranty free of charge all this information is online you peplos are so lazy to ck thanks