I've been on Yasmin before and like you, became severely depressed and suicidal. Your severe period pain could be caused by a condition called Endometriosis, (unless it's already been ruled out) which is where the lining of the uterus, building up to a period, grows abnormally, often into the fallopian tubes.
I would agree that you don't opt for hormonal treatment, as this method obviously does not agree with you. I stopped taking the pill years ago and basically think it ruins the body and mind. How does your GP know it's a hormonal imbalance?
Unfortunately these days, we have to be proactive in helping ourselves, as doctors and GPs tend to offer few solutions to problems. I have Fibroids and I really don't think they can just disappear, it surely must be something else like a cyst. When you have your next appointment, try to be more forceful, afterall, it's your health.