ok, my first thoughts are that CBT might not be right for you. Does she only practice CBT or does she have other modalities? It sounds to me like you have in earlier life suffered abandonment or loss which has affected how you feel about attachment? If this is the case, i strongly urge you to consider finding a therapist who can help you with trauma.

CBT has it's place, it is good for changing ingrained negative thinking and behaviours but it won't even begin to touch trauma. Because if you are acting out from a place of trauma, you literally have no control over your responses ie the fear of perceived abandonment and the frantic effort to avoid attachment in the first place. Your brain acts on perceived threat in a millisecond and it's so quick you're not even aware of it until you've acted instinctively. Essentially your brain is doing a flight,fight,freeze response. CBT isn't going to be able to touch that- if that is what's happening.