I was in a similar situation...basically still am. For a few months now, I couldn't really focus at all, everything gave me anxiety at work, if I read a sentence from an email and didn't understand it exactly at first my anxiety sky-rocketed and so on. I also had issues getting up in the morning and had also some conflict with my boss...I was taking a lot of sick leaves. At the end I resigned, because I didn't feel good there, wanted to leave for a while, but the conflict and the depression/ anxiety added to it too. Maybe in another situation I could have got a longer leave for depression. I'm still a bit frustrated about this.
I've also been trying to explain it to my doctor but she never offered the idea of longer leave. Anyway now it's too late for that.
I understand that it's hard to explain this to the doctors, I've had the same issue, felt like she didn't understand the fact that I actually couldn't work. Still can't. But it would make sense though to try to explain.