Is it worth fighting an emplyer for unemployment when they lie about the circumstances?

I was employed at a chain grocery store and had to call off sick one day from work. My company handbook states that if you need to call out the procedure for calling off is to call the manager at least one hour prior to your shift. On this one day I was sick and called in 5 hours prior to my shift and I talked to my supervisor and the stores manager I was told by the manager that I needed to find my own replacement or come in myself and If I couldnt find a replacement and was unable to come in I would be discharged. the department I worked in only has a few employees and which the majority of them were already scheduled to work. I couldn't find a replacement and was in no way able to go in. So I was terminated. I filed for unemployment and was sent a declined benefits letter stating that my employer said I didnt follow call out procedures that I never called in at least an hour before my shift. I filled out the appeal and sent in a copy of my phone record showing my call into my work the day of my termination showing I called 5 hours prior to my scheduled shift. I also had my friend over that day helping me with my children since I was sick who heard me call into my work. Is my phone bill and witness enough evidence to win? do I need a lawyer? cause I really cant afford a lawyer with not working. and Is it worth fighting my former employer? I feel like it is so unjust for them to fire me for being absent with no previous warning and with following the proper procedure but I feel like an employer even though they lie will automatically win in an appeal? any advice would be much appreciated!