If Spotify is the only app running slow while others work smoothly, it's usually not a network issue. Try completely deleting the app and reinstalling it - sounds basic, but it helped me when some files got tangled up in the cache. Before you do that, log out and write down your login credentials. After reinstalling, it should run fast again.
If that doesn't help, check your app settings under "Storage" or "Cache" to see if huge amounts of data are stored there - sometimes junk builds up. You can also try turning off the auto-download feature if it's on. Some versions of the app also have issues with older Android or iOS versions, so check whether a system update is available. If nothing works, I'd contact support - your account could have a glitch that only they can fix.