I have no solution for your current problem but I can tell you how to greatly stretch out fan replacement in the future. I have put all my fans on a timer with 30 min maximum run time. That is plenty of time to exaust what ever is ailing you in the bathroom. This will probably stretch the live of your fan bearings by a factor of 10.
If your fan is like the many I have seen, it is probably worn out by thousands of hours of senseless runnning.