Yes， you can use COBRA from your "soon-to-be former" employer.

I was extremely fatigue due to menopause. But doctor did not give me any sick leave. I struggled working and working...... finally I was totally falling down. After surgerying, I still could not be able to return to work. No doctor wanted to take care of me except myself. Suggest you see a doctor who can evaluate your fatigue rate then he can absolutely provide a sick leave. Other way you  could use COBRA from your "soon-to-be former" employer.