I feel so sad reading your post, because you sound so miserable! I know that you can't be nearly as bad of a nurse as you think you are, or you would not have survived three years and three different jobs without making a major mistake.
Take this for what it is, the opinion of someone on the internet who has never met you and knows only what you have shared in your post about you, but I think it sounds like you have very deep issues with self worth that probably go back many years. I, too, struggle with self confidence when I'm working as a nurse, and I have been a nurse for 23 years. However, I do not beat myself up or doubt myself nearly as much as you do. My heart goes out to you because going to work must be sheer torture for you under the current circumstances.
You mentioned that you sought help in the past when you suffered from severe depression. If that therapist was competent and you feel like he/she helped you, then I would go back and commit to a much more long term course of therapy. These kinds of issues take years to develop so most of the time they take months or even years to resolve. If that therapist was not helpful, then keep looking until you find someone that you feel that you can trust and who you really feel understands and can help you.
If you feel that there will never be any redemption at your current place of employment and that you will always feel insecure and unliked there, then stay long enough to where it won't look really bad on your resume' and make you appear to be too much of a job hopper, and then move on, but preferably AFTER you have received intensive, long term therapy and have started to overcome some of the painful issues in your life that keep you from being happy and successful or you will likely find yourself in the same situation again.
I wish I could give you a big hug. You sound like you are in a lot of emotional pain, and that you could greatly benefit from competent counseling and building your sense of self worth to a point where you can believe in yourself and be happy. I wish you all the best and pray that you will find joy and success very soon.