Just saying if it was mine I would not be driving it at all. If she/he keeps driving it they might as well start looking for a engine. If you keep driving it your are going to fry it, if you haven't already.I would honestly take it to Franklin to Gants. They won't rip you off and your problem will be fixed in a reasonable amount of time.
The question is; not whether the fan is turning alright, but rather is the fan kicking on when it starts getting hot? If not you have a fan, fan relay or an electrical problem. Nevertheless you do not need to be driving it until you find out and get it fixed.
If nothing else hot wire the fan to where it runs all of the time until you can find out exactly what the problem is.