Have you considered having two sessions a week, would that be an option? You might just need more support to do your best- I do.

Also, I would definitely support your idea of telling your counselor this, and want to add that it's normal and common- why wouldn't you relish the hour where you have a devoted, caring, helpful listener?

Hopefully she can help you both with concrete steps to enjoy your life outside therapy better as well as supporting you in therapy so that you get to a place, when you're ready, where you grow out of your needy feelings for it. Nothing wrong with feeling that way, in my experience, it's something to accept and trust that you'll get through it with work and time.