It's a really sick fixed/intrusive thoughts process, and you really need to get help and not act on this. This isn't what love is, and if you are linking pain with it you're putting yourself and your therapist in a very dangerous position.
I know BPD can be difficult, and your past may have you seeking love in the wrong places but these urges and thoughts and desires are not normal or okay. They aren't love. Wanting someone to know and feel your pain is selfish and beyond cruel. You really need to reach out and get help and not hurt the person that is trying to help you.
They are a professional, they are open to hearing your struggles, but you are breaking their trust and hurting them if you act on any of this. It could quite rightly get you sent to an institution or jailed and it will likely traumatise the therapist for life. Noone could ever perceive giving skin and blood to someone else as anything other than sick and evil and cruel. If that's your intention get help, please.
You can have dark compulsions and thoughts and it's okay to need help but to want someone to share your pain and sickness under the guise and gimmick of love, it's so wrong, words can't express.
Please get help, write and journal your thoughts, stay away from the sick suicidal TV sites, get professional help for this, and find coping strategies that won't hurt someone.
Kindest,