Would I have to unlink my other accounts first to create a new bungie account? I ask this because when I go to create a new account it wants me to sign into one of the systems; Steam, playstation, ect...
Yes, but the process is convoluted. You should unlink one account first (I recommend Steam) then use that to create a new Bungie account. Then log back into your old account (via PSN) and link a throwaway account (ex. a fake Steam account), log into that throwaway account, then unlink your PSN account. Finally, log into your new Bungie account and link your PSN account to it.