External hard drive doesn't work on iMac, does work on PC

Hi everyone.

I have an external hard drive which is formatted with ExFat. I recently put all my stuff on it as my MacBook Pro was sent to repair. So it obviously works with OSX. I also put stuff from my PC, and have tested it several times. Compatibale with both! I then left it alone for a while and tried connecting it to my iMac. It doesn't read it, not in desktop, not in Finder. I went to Disk Utility and there it is, but unable to mount. I tried verifying it and it said it needed to repair. I repaired, but it quit the repair and said that I needed to format the hard drive. I tried connecting it to my PC and it works like a charm. I can't, for the life of me, figure out why my PC can read it, but my iMac cannot, since I've used it with both just two weeks ago. I tried several USB ports, no luck. I tried pretty much everything, and since I have everything on it I'm in despair, as I have absolutely no free space on my PC, so I can't transfer my data to that, and I'm fearful that the external drive will collapse any minute now. ANY suggestions?

P.S. I recently updated my OSX, still no luck. And I might want to add that the ExFat is a partition, the only partition on my external, taking up all 1 TB. But again, I used it just as it is two weeks ago without any issues.

Magnus