I was just walking to a quest of mine leaving Whiterun when I a saw a dragon flying so I decided to kill it. I noticed it had a name, Krosulhah, and it said "You will die". I looked it up and saw that dragon is from the Dragonborn DLC. I don't have the DLC since there is no boat to take me to Solstheim. Is this a glitch or do I somehow have the DLC?
This is more than likely a bug
As with most game developers, Bethesda factored some upcoming DLC changes into their standard game updates. As such it's likely the data for this dragon is stored within the game installation on your Xbox thanks to an update, but a bug has allowed this hidden content to be pulled live into the game.
That's the only reasonable explanation I can think of for DLC exclusive content to appear within a vanilla game.