Do apply for unemployment. If you meet the hours worked requirements you may wualify. Then when your morning sickness passes, you can move on.
In future, if you have something that may prevent you from fulfilling your employer's requirements, and the reason is illness, talk
to your doctor and your boss and try to find an acceptable compromise. "I get sick in the morning - can I work evenings?" Normally the cause for a reasonable boss punishing you for such things is - whether you are sick or not, the customers have to be served, and if you are scheduled and don't report for work, the operation suffers.[@ya girl dakota]