There’s never been a test for a specific cold virus because it isn’t cost-effective. They generally mutate quickly and they don’t hit hard enough for treatment to have to ID the virus.
If you really need to know, a PCR can ID most infections, but they cost something like $200+ to run, not just a dollar or two.
So do you know what the “rapid antigen” test is looking for, for COVID?
I can see what PCR is, as far as replicating a testable blob of DNA. What do you do then? Run a Blot?