1997 Toyota Carina E Sli Leanburn is overheating?

About a month ago I noticed my temperature gauge was higher than the normal point. When normal it sits around half way. This time it was 75% up and heading for overheat. There was also some smoke/steam coming from under the bonnet. So I got home, parked and waited for the car to cool down. I got some antifreeze and some water and filled the radiator. Car ran fine for a month. Then tonight, I noticed the smoke/steam again and this time the temperature gauge was in the red and peaking. I stopped the car. When I got out I noticed water pouring heavily under the car and even a little through the front grill. I again waited for it to cool down. After a while I checked the water underneath again and it had stopped but there was a wet patch around the length of the car underneath and a heavy wet patch under the front of the car. Once it cooled down I filled it with water and antifreeze and drove home. I was close to home so it didn't overheat in that very short trip. Any suggestions? I've heard of silicon rad-fix options, breaking eggs into the radiator and all that. I'm happy to get it checked by a mechanic but I'd like to know what the likely problem is before I go there and if it's an expensive fix. It's an old car but a very good driver and very reliable and I'd like to keep it.