Appeal deadline questions after an unemployment denial (update)

My claim was denied after 22 weeks of waiting, and the letter says I have a short window to appeal. I am in Albuquerque, in case local advice matters. My employer's version of events does not match mine, and I have emails that show it. Should I ask someone for free legal help?

I printed my emails in order and wrote a one-page timeline. The hearing officer kept going back to it.