Can't be sure what you're problem is with the usb stick becoming corrupted.
Although, you can backup a whole operating system yes. The most suitable program would be `dd` which allows you to take snapshot type backups, literally cloning the whole disc image to a file.
You would want to boot from a different operating system (one that is already installed to your internal hard drive because files will change/movve around when the usb stick is in use as an OS).
For example if your usb stick comes up as /dev/sdc when it's plugged into the computer on your main operating system:
# dd if=/dev/sdc of=/root/backup.img
This would create a cloned disc image of your usb stick (kind of like an .iso file).
In the event you needed to restore it, you would simply swap the in-file and the out-file. So that it writes the image to the usb drive:
# dd if=/root/backup.img of=/dev/sdc
Make sure you write to the correct device.
When you use the program `dd` it literally copies byte for byte and will include all partition and filesystem information which can be useful for backing up an entire operating system.