Dear JustApsychologist,
I think you have amazing stats. and credentials and I can't imagine how hard it must have been to be such a successful student and deal with mental illness at the same time. I think it's amazing that you've discovered what makes you happy and I can only encourage you to pursue your dreams. I am sure you will accomplish them. You are really young and have your whole life ahead of you, there is no reason to think that you won't accomplish your dreams at this point in time.
I think its unhelpful to think what will happen when you get accepted and worry about failure due to your illness or lack of confidence. The fact is that you succeeded well in your studies up till now and you didn't fail. On the contrary, you shined.
The application process is stressful and alienating for everyone however, having panic attacks and severe anxiety when writing your SOP and letters to POI's just doesn't feel right - as you said so yourself.
I'm sorry to hear that you have no one to discuss this with in real life and going through this without support can be very lonely. Is there a colleague/advisor/supervisor/counsellor you can talk to?
I'm wondering how having support and someone to speak to during the process might make things a little easier.
Best of luck,