The false negative rate of the rapid influenza test is around 50%. It can tell you that you have influenza but it can't tell you that you don't have it.
And the additional note would be that later, when I had extensive direct contact with someone COVID positive, I had minor symptoms lasting two or three days. Which at least somewhat suggests I had an immune response of someone who had it.
No it doesn't. Most COVID infections are mild. And someone who recovers from actual COVID should have had mucosal neutralizing antibodies in your upper respiratory tract and neutralizing antibodies in your blood, so you shouldn't have had any symptoms at all.
If you had extensive direct contact with someone COVID positive and didn't take precautions then you just got kind of lucky. You weren't immune.
They’ve found extremely low numbers of possible cases in your state. The numbers found are very close to the expected false positive rate.
Meanwhile there was also an unusually bad flu going around at the same time affecting a high single digit percentage of the population. So ok it’s not impossible you caught COVID. There is a small but real chance, but it’s probably tens or even hundreds of thousands to one against.
https://www.cdc.gov/flu/professionals/diagnosis/clinician_gu...
There's also a lot of other cold and flu viruses other than influenza, and just a normal rhinhovirus cold virus can cause bronchitis or pneumonia.