How is your external disk formatted? Get Info on it and look at the top section for format.
If it is NTFS then you cannot write to it because you installed software that allows you to write to a Windows disk. That software needs to be updated to work with El Capitan.
A better solution would be to format the disk as OS X Extended (Journaled) so you don't need any third-party software to write to the disk. You will have to move the data off of the drive, format, then restore the data.
Besides not needing any third-party software to use the drive, Time Machine cannot back up the NTFS drive. So, you would have to backup your iTunes Library independent of your TM backup, if you are using that.
Both Seagate and WD have been bundling software on their drives that installs this third-party software instead of telling you how to format the disk for your Mac. You should contact them about an update for that drive if you still want to use a Windows-formatted drive.