There used to be a way to “appeal” getting fired, I’m not entirely sure if that still exists, you should’ve gotten that info when you were fired but if it was over the phone I’d think it would’ve been mailed to you. Call HR and ask about that process if it does exist.
If not, and you think it’s worth pursuing, hire a lawyer and sue for wrongful termination.
It still doesn’t entirely make sense that HR wouldn’t know you were sick if you called in, that their “assumption” would be grounds for firing with no proof, that they wouldn’t come to you about it before escalating, etc.