I just got Keening in the Odrasol Tower in Dagoth Ur. Now every time I go to equip it it says "Keening has dealt you a mortal wound" and it kills me. Does anyone know what I should do with Keening, or if there is anyone who I should give it to (quest-related)??

It is related to the Main quest, simply keep the dagger and play the main quest. You need wraithguard (a gountlet) given to you by vivec after you have completed a big part of the Main quest.

Put it on a shelf in your house. Don't use it again until the point in the main quest where it becomes clear to you that you must use it.

If you want to know more, put a thread in Spoilers.