Go to your downloads manager (press the middle button on your controller(the one with the big x), go to the left most tab, select active downloads).
What's it say? It should have the item listed. see if you can select it and get it downloading.
Heads-up: sometimes DLC won't download if you're doing certain things like playing that game online. I'm not sure about COD, but you might have to take a break while it downloads, if you do find it in the manager.
Post back if this doesn't solve anything ;) Hope this helps
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