Unemployment Question?!?

So here is the story. I have an older sister who has been battling depression for a long time. I got a phone call to get the hospital back in Sept 2010 to get to the hospital ASAP that my sister hurt herself. I was out of the office on my lunch break. I immediately headed there. What was I suppose to do? I had an emergency. So while at the hospital I emailed my temp agency that I had a family emergency. The email failed to send because of a wrong email address so I forwarded the email to the company boss that the temp agency had me working for immediately that same day. So I thought all was well because they didn't call or email me back yelling. Well the next day I sent another email to DHL the company I was working for through the temp agency asking for a few days off because I was overwhelmed with what was going on & needed to be with family. That was 9/22 I sent the second email. Needless to say they called me back & fired me. So they told unemployment I had quit on 9/22 but I sent unemployment office both emails with the date, time, subject, & body of the email.What does everyone think? Will I have to keep fighting or will Unemployment see that I was fired unjustly & the company lied? I can't believe the company would lie like that to avoid paying me unemployment. I am just now filing too because I had no idea I could get unemployment for being fired. A friend actually told me to file! So that's why I am just now filing for it incase that makes a difference. Any help would be appreciated. Thanks!