It would mean that you are heartbroken. You can be torn up over something as well. This would imply you were very upset with what happened. The over apart in the expression is synonymous about (at least in the sense of being torn up about something).

Also, a different expression is just "to be torn". "I'm torn as to what to do. I am unsure what decision to make. I'm torn between buying the red shirt or buying the blue shirt."

Being torn up over someone means that you are upset/devastated/saddened and hurt about someone. Frequently used about a romantic partner who has left or betrayed someone, but other uses, too, anything that can make you feel like you're falling apart (figuratively!). Here "over" means "about" (that person).