After an hour in the dark of my bedroom, I still see points of light, like "snow" on a TV. Are these caused by present photons, the random firing of retinal cells, or lingering images?
They are random firing of the cells,.
You see more of them against the dark background, unless there are enough of them to see in normal lighting it's nothing to worry about.
Lowest energy cosmic rays (still 10^9ev) are about 1 /m^2/s at sea level
I don't know what fraction would trigger an event on your retina but they are going to be rare enough (because of the area) that I don't think you would notice them