How can I get twitter notifications on my iphone 5

I can't access the Twitter notifications I receive on my iPhone 5. I get them on the lock screen, and there's a red dot with a number on my Twitter icon, but when I open Twitter, there's nothing under "Notifications". What gives? I was trying to customize so I don't get tons of spam tweets and I guess I turned something off? I used to be able to access the info.