Your question is confusing because you appear to worry about tardiness from a sleep disorder but confuse the matter with stating you're a lone female. If you're 'disability' is causing you to be late and you're getting disciplined and written up, you may have to seek an accommodation where you're allowed to be so many minutes late. These are often difficult and tricky situations so you're best served calling an employment attorney.
You have almost nothing invested in this new job and the new employer has virtually nothing invested in you. The legal path you are sighting is long, emotionally grueling, and hard to successfully navigate under the best of circumstances. Dealing with an employer who is lying in wait for a clean and legal opportunity to fire you is no way to live -- and that is a very predictable outcome here. Disabilities don't make employees bullet-proof; they only out employers to the burden of patience, documentation, and skilled legal strategies.
My advice: get yourself a job where your shift starts later in the day. Life will be better.
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