I drove about 10 minutes and white smoke came from under the hood. The gauge did not show it was overheating. I let it cool down and I took the lid off to see if it needed water and it didn't. ( I kept the lid off) I turned the car on and the antifreeze started overflowing from the top of the radiator slowly. The backup was still full. Its spurting from somewhere because it has fluid marks on the hose. I don't know if this has anything to do with it but... I took my car for an oil change about 2 months ago and they didn't put the cap on right. It was sitting on the top. There is black stuff around the top and radiator. I checked the oil and I had to put about 1/4 of a quart of oil in it.

Sounds like a head gasket has gone bad. I bet if you take it to a shop and they run a hydrocarbon test on the radiator they will find combustion gasses present. Indicating a failed head gasket.

Sounds like you have a coolant leak and it is spraying on the engine or exhaust. You will need to find the leak and fix it.

As smoothy said, it could also be a head gasket. I would first look for a leak based on the fact that you said white smoke is coming from under the hood. If it's coming out of the tail pipe then it's a head gasket for sure.

Sounds like a blown head gasket. If so, the aluminum head likely has warped and needs to be machined. Also, have the valves checked for damage. This is the ideal time to replace the timing belt and water pump. Make sure you and your mechanic read the Owner's Manual on exactly how to drain and refill the cooling system, in order to prevent air from forming in the system. Improper filling often results in a blown head gasket.