1995 Lincoln Continental

Yesterday the belt broke on our car. The car began to overheat, the power steering went out, the battery light came on as a result. We later discovered what the problem was, but only after continuously pouring water into the radiator because we basically had no idea what we were doing!

Ultimately we had put way too much water into the radiator and we noticed that it was dripping out of the exhaust pipes. We had the car towed home, fixed the belt problem, changed the oil, filled the radiator. The PROBLEM now is we are getting white smoke coming out of the exhaust. It has been very rainy here today so I am sure that the over-watering has not had time to evaporate. We don't smell coolant from the exhaust except for perhaps a very very slight tinge of it (and you really have to be concentrating on it.) Please help! What are we missing this time? . And thank you!