Conveying the idea of "balancing conflicting interests"

cognitive dissonance is one possibility

cognitive dissonance

noun

: psychological conflict resulting from incongruous beliefs and attitudes held simultaneously

Merriam-Webster

EDIT

Having seen FumbleFingers' 'conflicted', I think that's probably closer for your context.

You feel as if you were on the horns of a dilemma. In this case, not that the consequence of either decision would bring you an unpleasant result, but discarding one of them would.

• dilemma (noun) "a situation in which a difficult choice has to be made between two or more alternatives, especially equally undesirable ones."

am·biv·a·lence
amˈbivələns/
noun
noun: ambivalence; plural noun: ambivalences
the state of having mixed feelings or contradictory ideas about something or someone.