Obsession

[Sonia]

The state of being besieged; -- used specifically of a
person beset by a spirit from without.

[Couch Potatoe]

An almost insane desire, [longing], or burning [lust] for someone or something. You feel like without that thing or person, you are not complete and cant [cope], or- in extreme circumstances- live, unless you have the object you desire.

[PussyCat]

[ob]⋅[ses]⋅[sion]  /əbˈsɛʃən/ Show Spelled Pronunciation uhb-sesh-uhn

–noun 1. the domination of ones thoughts or feelings by a persistent idea, image, desire, etc.

[Couch Potatoe]

[Something] that you [think] about or do all of [the time] over and over.

[Dave Paprocki]

[To love] in a [fanatical] way
To lack the ability to leave a person alone
An animal that never quits [the hunt]