Product:Macbook Air
Problem: memory is running short and I am experiencing that spinning wheel.
Solution Attempts: Thought about deleting the music from the computer but a message pops up letting me all my music will be deleted from my other devices.
Concern: I am not very savy with computer and fear if I delete my albums that I will loose them forever.
What Can I Do?
MacBook Air (13-inch Mid 2013), iOS X Yosemite
Your computer has two primary types of memory. "Memory" strictly speaking is the amount of temporary storage space used to boot the computer, run applications. It is usually called RAM. "Drive storage space" is how much space you have on the computer to store files such as music, applications, etc. They are two very different things.
Breachballing can be related to low RAM but can also be due to iTunes just trying to do a lot of things at one. iTunes has become more and more bogged down with all the things added to it. If you just activated Apple Music it could be slow because iTunes is now analyzing all the music files and also transferring some to Apple's servers.
Beachballing is unlikely to be related to low storage space unless you have filled up your drive to almost capacity and iTunes has to look for bits and piece of storage everywhere to store files. That's not the say you need not be concerned about your library storage but your post is therefore inconsistent in the topics it needs addressing. I think, however, many users are finding the drive storage afforded by laptop computers is fast becoming inadequate for modern use and are resorting to storing their libraries on an external hard drive. If you do this you need to buy two, one for storage and the other for backup of the first. Apple does offer re-downloading currently but there is no guarantee that will last forever and the only way you can be certain of always having a copy of media is to keep at least two copies on two separate drives.
How do you know that memory is running short?
Running of of memory
