Is my USB drive broken, or is it my MacBook?
If it happens to your drive only with your macbook (on both OS X and Windows) and works fine with other machines, then the problem is most likely your USB port. 

I suspect that it is supplying more than the stipulated voltage (5V ± 5% for USB 2.0) and your device must not be sophisticated enough to only take what it needs.

You can check this using a multimeter and a USB male connector (I chopped a spare USB extension cord when I needed it). It should register the correct voltage and if not, there's your problem.

If you're going the chopping an extension cord route like me, here is what it will look like if you strip the wires (image source)



The white and green wires are for data transfer — you don't want that. The red is +5V and the black is ground. Connect your multimeter to those to check the voltage.