The concern and caring you are getting from your therapist are legitimate needs that have been unfilled and now you are finally getting that from someone. That is a good thing! It is what you need to find or create in your other relationships outside of therapy. It would be nice if we could find a good therapist who is able to fulfill your unmet needs and then just build your life around that person, but it just would never work. Even if you find one person in real life who can give you love and concern, it might not work if that is the only person - they wear down and can't keep it up forever, so you have to learn to build relationships like that, and keep building them, and finding a balance of giving and receiving.

Yes, you do need to talk to your T about this, but don't worry. This is normal in therapy and you won't lose him because of it. He can help you put some of that energy into your life and learn how to build something that you will be able to sustain.