my computer died. how do I retrieve my itunes library if i back up my phone to the cloud daily?

My pc crashed. When I access my iTunes account, the only music in my library is the music I purchased from Apple. I had music purchased from other sites and also music ripped from CDs. I back up my phone to iCloud daily. Can I restore my iTunes library from this backup? if so - how? I would try to restore from my phone but I'm afraid that I'll lose all my content.