03 Monte Carlo smoking

My car recently over heated, I put coolant in it and
water in the radiator. Went to go get something in
town and it started to smoke. The person I bought it
from said that the water pump could go at anytime.
He had purchased one but at the time that was not
the issue so it's been sitting in my trunk. My car has
overheated before but when I put water and coolant
in it , it was fine. Could the water pump be the
reason or is there a deeper
issue? Also, when it overheated I let it cool down
and I had to drive home, I watched the gauge and
had to pull over a couple times and shut it off. But it
never over heated and I was only about 8 mile from
home. Just thought I'd say that to give you a better
idea of what happened.