Got fired for "attendance issues" after using all my sick days when I actually had the flu

So I just got let go from my job of 3 years and I'm still processing it honestly.

I work - worked - in customer service for a tech company. $48k, fully remote, pretty chill job overall. Or so I thought.

Two weeks ago I got the flu. Like actual influenza, not just a cold. Was completely out of it for 5 days. Used all my remaining sick days (had 3 left) and then took 2 unpaid days because I literally could not function.

Came back last Monday and my manager scheduled a meeting. Thought it was just a check-in or whatever. Nope. They're letting me go for "excessive absenteeism and failure to meet attendance expectations."

I used 5 days. For being actually sick. They're acting like I was just skipping work to chill at home.

Asked HR what the policy actually is and apparently if you use more than your allotted sick days in a quarter it's considered a performance issue. But like they only give us 4 sick days per quarter? So if you get actually sick once you're basically screwed.

Now I'm scrambling to figure out what to do. Tried seeing how long my savings will last and it's like 2.5 months if I'm careful. Need to file for unemployment but idk if I even qualify since they fired me for attendance.

Already updated my resume and started applying places but the job market is rough right now. Took me 6 months to find this job back in 2021.

The whole thing feels so unfair. I wasn't faking. I had a doctor's note. But apparently that doesn't matter because I went over some arbitrary threshold they set.

Anyone dealt with this before? Can they actually fire you for being sick or is this something I should fight? I'm in an at-will state so idk if I have any options here.