This was the case when I had it last winter, according to a physician friend.
I won't be able to explain it eloquently – definitely had brain fog during that conversation – but he described something about how having the virus arms your immune system to generate custom antibodies for different strains, while the booster simply provides a set of antibodies for existing strains.
Either way, at that time they were advising something like a 90-day period of enhanced immunity after having the virus, during which a booster was both superfluous and not recommended. Not sure if it's changed since last winter, though.
Feel better,
@Shadrach. That virus is no fun. The brain fog's the worst!