Yeah you should be able to use the Coeurl mount.

I would check the Calamity salvager in any of the major cities. All I can think of is maybe you dropped it instead of using it?
If you did he should be able to give it back to you. If he doesn't have it check your inventory or your mail, you have to get the whistle from the moogle mail than use it from your inventory to call the mount.

If none of that works you might have to put in a request for a GM in game to help you.