I have two YouTube accounts because I signed up with two different email addresses. I ordered YouTube premium on one of the accounts and even though they are both my accounts the other one says it only has the old YouTube. I need my premium on both.

There are a couple options here... if you bought it at YouTube.com then signing in to the correct account via the YouTube app would work (aka sign in sign out)... best experience though with up to 6 Apple IDs is by using family sharing, so... if that is how you bought the premium subscription (through App Store subscriptions) and your current Apple ID doesn’t authenticate your purchase then (if you family share from one Apple ID to the other) that would share the purchase but cost a little bit more and add up to 4 more family Apple IDs to use that subscription. If you have no intention on using both Apple IDs then sign out of the iTunes & App Store with the current Apple ID and sign into the one associated with your original subscription!