I am feeling discouraged

Hello, My name is Liz and I graduated nursing school one year ago and am feeling very discouraged and would like some advice/hints.

I graduated nursing school when I was 22, I am not 23, which is still pretty young for a nurse. I also never held a job before being a nurse.

As I said I graduated nursing school one year ago and since then I have only worked 7 months and been fired from two jobs. When I graduated nursing school, naturally I wanted to work at a hospital. I had one hospital interview and didn't get the job. I continued, and continued to apply, but I live in a city with LOTS of nursing schools and strong competition to get into the hospital setting.
So I started applying elsewhere and took a job in an emergency psychiatric setting. I worked there for 4 months before I was let go. Nigh shift was sending my boss, and management lots of e-mails about me, which held some truth, but were mostly far from true. They didn't really want to hear my side of the story, and instead allowed me to resign.

The next job I took was at a nursing home. They fired me shortly before my probation period was over. They said I wasn't team oriented enough, or proactive enough.
Since getting let go I have been reading up on professionalism. I feel like I have learned a lot and can see some of my major mistakes. I acted like I was not confident in my work and asked my co-workers too many questions. Talked about things I shouldn't have. I am not as assertive as I should be as a nurse, but as I get older I continue and continue to be more and more assertive. I did not take enough pride in my job. I did not continue to study and work on keeping up my knowledge base.

I've decided to primarily try and get into the hospital setting, and am even willing to move to a different city. Does this seem wise considering my past history?
Does anyone have any feedback for me I would be very grateful! I love nursing and am not willing to fail at being one.
Thanks so much!