Your new cosmetics will be available in the Collection tab in the game. The Hero Frame will be under Frames, and your new Costumes under Heroes. To select a new Costume for a specific hero, navigate to that hero, click on the arrows next to their art on the right-side of the screen, and then hit ‘Favorite’.
If you were already in the Collections screen before purchasing Premium, make sure to go to another tab in the game and then back to Collections to see your new cosmetics.