You don't have to use the WD backup software (or any software that comes with any external drive).
It sounds like what you want to do is copy the contents of one drive to another.
EasyPezzy!
No offense,but it sounds like you are not a computer expert (that's great! You hit the best place on the Internet to learn!)...
you said, "have used up a lot of my memory with music that I've downloaded "
It is not your "memory", it is your storage space on your main drive... Flashdrive/ssd/hard drive-that is called storage.
Now here's the thing-you don't have to use Western Digital's backup software. I didn't even look at the bundled software that came with my WD My Book 16 Terabyte Drive (or 12TB-I forgot what I have...Doesn't matter. I'm not even close to filling it. I remember its big).
If I am wrong let me know and we will go from there, but it sounds like you know what you want to back up. In that case,the WD backup software (any backup software) gets more in the way than being useful.
Just open File Explorer, plug in the WD drive,plug in the flash drive,and wait a second for Windows to recognize them and you are set.
Now Windows File Explorer will see the WD external drive as just a drive. It will see the Flashdrive as a drive. Now jusat copy and paste in File Explorer.
you can copy individual files,or the whole drive from the Flashdrive to the WD MyBook drive and you can rest easy your music is backed uped.