Funny you should ask this question today, I just had my Grand Am in the shop for this exact same problem. (mine is a 99) I couldn't find the problem anywhere when I looked under the car so I took it in to a repair shop and come to find out the problem was due to a leak in the seal on the timing chain cover. Not sure if this is what is wrong with you car because in 99 Pontiac released a new model for the Grand Am. I will tell you for certain that the problem is not a joint or the drive shaft since these two parts do not carry antifreeze. One other thing to check would be your hoses. (wait until your engine cools) Do they feel mushy do you see any seeping around where they attach to the engine or to the radiator? Is there fluid in the reservoir tank?
In my case $550 a new seal in the timing chain cover and the problem is solved.