

The “flu shot” tends to be variable in it’s effectiveness from year to year. It’s a guessing game the CDC play with those virii. They are/were trying to guess what the vaccine needs to be months in advance. This year it seems they missed a bit and it didn’t work quite as well.
The future seems bleak on having those shots available for the foreseeable future.
Most guns shows have FFL dealers on site. Those guys are definitely running the federally and state required background checks in a little room in the back somewhere. And if the sale happens inside the building, it’s even highly likely private sales get run through also, (you will pay for it-- someone has to make money off of it). The Paperwork Gods must be appeased no matter what.
But depending on the state/county/city often you can do a private sale in the parking lot with someone that doesn’t get the check. This is not universal across all 50 states. Some states, like California require all firearms transfers to go through a licensed FFL.
YMMV