How to write a letter to a Judge asking for leniency due to me having a health issue?

There should be legal aid in your area. You need someone to act as attorney. My opinion, from what you wrote, a letter will not help. They just don't care. Get a person, an attorney, to speak on your behalf. Maybe community service can be set up. I have heard that even c.service can have its troubles, so carefully obey or your life will be disrupted in another way.