I'm wondering whether maybe the problem isn't you or your T but the context you're both in. If I recall correctly, you see your T at a university counseling center that offers a fairly limited number of sessions, right? I was in a similar situation for a few years, actually with my current T who is now in private practice. She is an extremely competent therapist and a good fit for me personality-wise. I worked hard in therapy and was as transparent as I could be about my issues. We made some great progress on some family issues I was dealing with, but we really didn't put much more than a dent in my persistent depression, which I have been dealing with since I was thirteen. It just... persisted. I didn't have symptoms all the time, but the depression was always lurking right behind me. I sort of assumed that's just what life felt like for me.

My T left her counseling center job to set up a private practice a few years ago, in part because she wanted to do therapy based on what her clients need and what she can offer them, not based on what the center said was allowed. I used to see her every other week with no outside contact. Now I can see her twice a week if necessary (which I have been doing for the last six months) and I can call/email whenever. There is an element to all the extra contact that has helped initiate a giant shift in how I see myself and my relationships. For the first time, I can see the roots of my depression and (more importantly) I can see a way out. I also truly understand for the first time that the depression isn't my fault. I can do certain things to try to help myself, but sometimes it won't be enough to stop a depressive episode entirely, and that's okay. It doesn't mean I am bad or lazy or broken.

In some ways, the every-other-week schedule was almost harder than no therapy because sometimes issues in my life would get opened up and probed without me having the necessary support or closeness with my therapist to deal with them properly. I would encourage you to think about getting a higher level of care, if that is something you have the ability to make happen. Maybe find a therapist who can give you more than what you're getting now. This seems especially important if your current T is saying that they are not sure how to help you. Switching to a more intensive therapy schedule has been a fairly significant investment in time, money, and emotional energy for me, but finally being able to see some light at the end of the depression tunnel has made it so, so worth it.