Can i file an unemployment appeal?

I was medically discharged from the army in may, I filed for unemployment in june. I have a 2 month old son that we cannot afford daycare for right now with my husband only working part time. On my unemployment claims, I said that we couldn't afford daycare right now on my husbands salary so I was having to stay home with my son, but that as soon as I got a full time positioun, my husband was going to switch to night shifts so I could work and one of us would always be with our son. I can't work without childcare, and can't afford childcare without work!! I have been filling out applications & job searching the whole time, but they sent me a letter stating that due to availability, my claims were denied. Can I appeal to this? If so, what would I need to do/say & what are the chances of winning? Sorry, I have never been in this position before, thanks for any advice!