It wouldnt be a 9/16", so if its smaller than a 14mm, the 13mm would be it. (I am too lazy to go outside and run the car onto ramps to see what it is on our 97). You should use a 6 point wrench, not a 12 point wrench, and if its been put in really tight - its likely time to replace the plug with a new one. The thread is M14 x 1.50 I believe. The drain plug is one of the hex head items on the car that gets a lot of use; like being removed 20 to 30 times in 150,000 miles. So if the hex head or the threads are worn/mushed, or the plastic gasket under it is crushed, a new drain plug helps. Auto parts stores usually carry them, in one of the bubble packs they hang along the walls. Most of them also carry the plastic washers too.
And you shouldnt need to overtighten it, as is commonly done.