Your response to those circumstances is definitely normal. We all want to care about those who mean a lot to us. However, the therapy relationship is unique in that we aren't supposed to focus on our T's problems. It's totally about us. What is going on in their personal lives doesn't matter, unless it's affecting their ability to be there for us. It seems selfish, but that's why we pay

Also, is this possibly a way to make your T "need" you or idealize/come to appreciate you more? Are you attempting to make the relationship more than what it should be?