Music that I purchased isn't showing up on my imovie

Apple Music is DRM protected and cannot be used in iMovie. You can use iTunes songs purchased after year 2009.

—Rich

Is the music possibly stored in the Cloud, in which case it wouldn't be recognized by iMovie. Songs in your physical iTunes library purchased after year 2009 should be recognized or in any case you would be able to drag them from your library into iMovie.

-- Rich

I recently changed computers and an album I purchased in 2014 isn't available for downloading to the new computers. It was working perfectly on the original pc. The album is Somewhere Under Wonderland (deluxe) by the counting crows

The album is available on iTunes.

Have you authorized the new computer (iTunes/Account/Authorizations/Authorize this Computer)? Or perhaps you have too many computers authorized and need to de-authorize one or more.

Songs purchased on iTunes after year 2009 generally do not have DRM protection, so that should not be the problem.

Otherwise I don't know why the Counting Crows album would be unavailable for download on your new computer.

-- Rich

EDITED