As Kitty basically already said, Raid Tickets only carry over from your Gifts. That means you can bring 300 Tickets from PP rewards and 30+50 Tickets from Event Quests per previous raid event.
Any unspent Raid Tickets in your inventory are DELETED the moment you enter the raid main screen for the first time. This is also the reason why you can't see raid help requests of that event until you've visited the raid main screen once (anymore, we used to be able to see them and people would constantly get their Tickets deleted).