I'll lead with saying I'm not a handy man. I'm not an eletrician. That said, light bulbs in our house do burn out in various places fairly fast. The issue at hand here though is the ceiling fan in my master bedroom. If I flip the light switch on the wall to turn the fan on, the turns on just fine. It may work for a few minutes or even a few hours. One thing is certain: before morning, the circuits will blow and it will smell like something is or was burning. I've put tape over the light switch since we don't know if the issue is the fan itself or something more extensive than that.
I'm not sure if it possible with this information, but would replacing the fan resolve the issue? Some folks I've talked to (not professionals...just family) think it may be the fan motor.
One last thing. The wall switch next to the one that controls the fan will turn the fan light on and off. This works fine and has caused no issues.