Not if the job you were hired to do requires you to be there a certain number of hours per week that you cannot work because you have other responsibilities.
Check out the Family Medical Law Act. If you have worked at the job xx amount of hours you should be eligible. Employers are required,by law to give you 12 weeks a year for exactly this type of thing.
You also may be able to collect unemployment insurance, since you were terminated for someting that was out of your control.