My understanding is that vaccination protects against those side effects, although lack of good studies means we can't say definitively how good that protection is. There's definitely an effect, but the studies don't entirely agree on how strong it is. I think the best studies put the case rate at something like 1-2% of vaccinated people who get COVID experiencing Long COVID symptoms in general. (I don't think enough data exists to say how prevalent any specific Long COVID symptom is.)

So assuming you were vaccinated, try not to worry about it. The odds that you have Long COVID at all are pretty low, and the odds that you specifically get stuck with brain fog are even lower.