"Like I am miserably depressed, but at the same time I feel like I'm all shut down and apathetic and it's hard for me to make an emotional connection and answer her questions."

There's no "but" there the way I see it. Being miserably depressed is that shut-down fog of trying to find words and connect but nothing working quite right. How much does your T know about that apathetic feeling? If you express yourself better in writing can you and your t find ways to use that to your advantage? Maybe you can send emails or share journal entries or something?