I would like to chime in and share my own experience on this issue:
Before starting E, I did not have problems with anxiety/panic attacks - however, I did experience this sort of never ending, residual, treatment resistant depression that was due to my gender dysphoria. I went for physical and mental health treatment at the same clinic and they were wise enough to realize that dysphoria was causing depression and that that had to be dealt with through transition. When I first began transition, I was very euphoric - but after several months on oral E, WHAM, I began to be hit with all kinds of anxiety and anxiety-related symptoms... panic, agoraphobia, etc. And to be honest, no one really knew how to respond to it and I was like in perpetual what-the-heck mode... it was overwhelming to the point where if I could have been happy by de-transitioning, I would have - but I couldn't and I knew I couldn't because of the overwhelming depression, but I truly spent months trying to figure it out, and simply could not make sense of it. It got so bad to the point where I stopped driving and then eventually was hospitalized. I did a trial of Ativan which, as has been said, can be a great short term method of stopping a panic attack but is simply unwise to use long term. Further problems came when they tried to find a good longterm medication. I started with Celexa and ended up having a manic reaction and then the search was on for a good "mood stabilizer" which is a long story but suffice to say that a lot of them, i.e. Lamictal, actually messed with my hormones and caused MORE problems. Eventually with a lot of research and a lot of introspection, I've reached the finally conclusions...
*Living with life long gender dysphoria is traumatic. Trauma - especially trauma early on life - changes brain chemistry and makes the brain more vulnerable to anxiety and mood disorders in the first place. Since I have a family history of Bipolar, it just makes sense that I would suffer from depression that also has Bipolarish traits.
*As has been said, Estrogen can make us more in touch with our feelings - its like before transition, I had this pervasive depression which under E essentially "converted" into overt anxiety/panic.
*Estrogen, especially when its levels change, can cause mood / anxiety problems for anyone. I felt totally like I was alone in a black hole, in some other dimension, not like successful transitioners but also not like those who "regret" - until I began spending a lot of time reading the experiences of women who had undergone full hysterectomies and their experiences of HRT. It was then that I realized that it IS the hormones. Our bodies are all so unique and respond differently to hormones, that the levels, the amounts, type of delivery, etc. has to be tailored to everyone based on how she feels. Some providers get this - some are clueless.
*I found that, for me, I'm caught between a rock and a hard place. On the one hand, Oral E does the best job at creating changes that I want in my body - on the other, transdermal E stays at a more consistent level and I feel a lot more mentally / emotionally balanced. So what do I do? Having done Oral E for years, I sticking with transdermal for the time being.
In any case, what works is unique to each person. This is a tough issue to navigate, but you are not the only one, and I wish you the best.