We are having this same problem.
I updated from 3.8.5 to 4.1.1.
I uploaded a couple of images first and they went up smoothly.
Then I updated wpml-plugin and then the media library broke:
when I tried uploading a picture it multiplied into over 700 identical pictures that filled my library and I couldn’t stop the uploading process.
I read that WPML media plugin might be responsible so I disabled it.
Now when I upload something it seems to be uploading but it doesn’t show up in the library.
So at first it was WPML but now it seems to be WordPress.
Please help!