I don't know why this is a boundary-exploring information online about who you are curious about. Didn't she introduce the fact she had this boyfriend?

Don't you have a boundary that others can't tell you what or what not to do with your free time?

I'd be distressed over wasting my time over non-productive things too. What would you be doing if you weren't spending time obsessing over this?

This is a good idea. My therapist always tells me to go towards the direction of the anxiety, rather than away from it.

Going with it, instead of against it, can also help stop the pattern. These types of obsessions are driven by conflict. And going against them strengthens them

I think making it about 'boundaries' might be what is keeping you in this pattern as it is strengthening it by making it 'wrong'. The need to do it + the conflict about it doing 'wrong' (guilt) are the elements that make the OC loop.

Maybe explore why it feels wrong to you, then deal with the guilt, then give up just that one part. Then you will be left with just the need to do it without getting all distressed and obsessive about it.

Doing it isn't unsafe or hurting anyone. Your therapist's boundary is to not tell you a name, not to control you. If my therapist has a boundary that he won't listen to his favorite song with me in session, I am still free to listen to it to my heart's content outside of session.