While I cannot be certain -- my guess is that your appeal of your
Unemployment Insurance case is going to amount to 'your word against
your former employer's word. By all means, file the appeal --
doing your best to clearly, simply -- and truthfully -- state why
you believe that you were not at fault in your separation.
That said, because an illness was involved which left you with some continuing disability -- you might have more success filing a claim under federal law for employment discrimination due to disability
For example, under the Americans with disabilities Act, employers are
required to make 'reasonable accommodation' in order to employ (or
continue to employ) an otherwise qualified applicant/employee.
An Independent Living Center in your State
can assist you with this claim process -- and can also help you with applying for Social Security Disability Insurance
(SSDI) Benefits -- if you should wish to do so.
Let me know if you need more input. If not, thanks for the
opportunity to assist you... Please honor my efforts by pushing the
green 'Accept' button (located within this post -- above-right).
Adding a bonus -- should you wish to do so -- would be warmly welcomed.