What people think of as "your sign" is just your sun sign; you also have a moon sign, a mercury sign, a Venus sign, etc.. Your natal astrology is a snapshot of where everything in the astrological sky is, not just your sun. For example, I'm sun and Venus Aries, Luna Virgo, Mercuy and Jupiter Pisces, etc. The signs themselves, even those you don't have a planet it, still affect you and this can be seen most readily in the Rising sign and the Midheaven.
Astrology is one of my major points of study, so feel free to ask questions.