Yes. "I'm a prisoner of love" is correct. I am in love and it takes over my life. "I'm prisoner love" is incorrect and meaningless. The only way it would have meaning is if your last name was Love, you were in prison and somebody asked you to identify yourself. You could say: "I'm prisoner Love", just as you would say "I'm prisoner Smith". Otherwise, it is incorrect and meaningless, though some people could probably figure out what you are trying to say.

Yes "I am a prisoner of love" is the only one correct. However I do have friends called Ian Love, David Love and faith Love. I hope they don't get locked up.