A4T, I see why the CPN didn't encourage you to have counselling. Yes, I think you do need to have a bit of inner strength before you go into it. The two sets of psychotherapies that I had were extremely hard work, and from week to week I wasn't sure whether I would be coming back again. I don't know what sort of psych treatment it was, but I found myself digging very deep into myself and saying things that surprised me...and yet at the same time feeling as if I had known these things all along so they shouldn't have been surprising. And it was often very difficult dealing with the feelings. I called it 'opening a can of worms' and yes, I think you ought to go along with the CPN's advice for now and give yourself a chance to begining recovering before you start with counselling.
That said, however, my dealings with CPN, OT and NLP were never distressing in the way that the psych treatments were. Perhaps because all three of these people were out to help me find ways of coping and of getting pleasure and satisfaction in my life, so they were about support rather than digging away at my psyche and getting me to talk about painful things.
Whatever you do, by seeing the CPN or psych you are in control (even if you're not paying for it week-by-week). No-one will 'treat' you against your will. You are more in control now than you were a few weeks ago, simpy by virtue of having gone to the GP and started the ball rolling.
I, too, hated being labeled 'depressed'. It felt like I was inviting the world to come in and mock my failure as a person and as a mother. But of course the truth is that I was not a failure, any more than you are. I was ill. I had an embarassing condition - a bit like having greasy hair only a million times worse. And if you have chip-pan hair then you try different shampoos or conditioners, or change your diet, maybe get an easier-to-manage hairstyle for a few years. And if one day you forget or cannnot be bothered to wash your hair, why then you put on a big flamboyant hat and pretend it was deliberate!
Now, lists. Make them short! And make sure you have a few easily achievable items on them, so that at the end of the day there will be some ticks to encourage you. The dust will still be there tomorrow, it can wait a little longer.