If you're wrapped up with someone or something it means your involved with that person or thing, to the exclusion of other things.
For example:- She is all wrapped up with her husband and his problems.
If you're wrapped up in someone or something it means you're obsessed with that person or thing.
For example:-
I'm too wrapped up in my web site to get a proper job.
This photo shows a fence post that's all wrapped up with barbed wire. Or some barbed wire that's all wrapped up in a fence post. It depends on which way you look at it.
