Horology is the study of clocks. You probably meant astrology/horoscopes.

For the sake of horoscopes either is fine - the zodiacal sign changes from Aquarius to Pisces somewhere between the 18th and the 21th, way before the end of the month. And most people don't even know the hour that they're born in, even if relevant for the placement of the 12 houses (including the ascendant, the start of the 1st house), and commemorating your birthday a bit before or after has zero to do with it.

Source: I don't believe in astrology but I made some cash in my teenage years selling horoscopes.