What dies happen if I call for sick from my previous job and start a new job?

I am experiencing depression and special personal situations that hurt me alot. Currently I am working in a public school and I found a job a month ago. I am not able to work in the school with all of the pressure and stress at my work while that office job is much easier for me and my situation. If i call to my manager for sick leave, can I start the new job? What are the steps and rules about?

Looking forward to hearing from you,

Regards,