I'm starting a Redguard paladin build soon and was planning on joining the Companions. I was going to use Alteration and Restoration to spice things up but I feel like the Companions are strictly Warriors. Would it go against lore to join the Companions while using magic?

I dont think so. MY current war priest uses heavy armor and wields a mace in one hand. In the other he uses all restoration magic and alteration. He charges into battle bashing everything with his mace and leads the Companions. You'll be fine lorewise.