My understanding is one doesn't get unemployment insurance after quitting a job. So that information would not benefit you in getting unemployment insurance. But it sounds as if you have some problems with your employer that might constitute constructive discharge. I recommend you ask your question in the employment section of Avvo.
The information provided is purely for informational purposes, and is not intended to be, nor should it be, relied upon as legal advice. It is not intended to create an attorney-client relationship. You should consult with an attorney regarding your specific situation.