Its genetic. Meaning that your genes are causing the grey hairs, not what you do to it.
Its normal for your siblings to not have this either. My friend started going grey at 16 - 17. She thought it was stress, it wasn't, and she has since been coloring her hair every couple of weeks. Her siblings, who are 5 and 7 years older, have never seen a grey hair on their own heads. Even now, more than 10 years later, her siblings don't have grey hairs.
As far as the blow drying is concerned, that just damages the hair. If you have strong thick hair, and you don't overly process it, you are fine to dry your hair when it is damp. Not sopping wet straight from the shower, but damp. Get out of the shower, towel dry your hair, and let it air dry for about 15 mins, depending on your specific hair, then go ahead and blow dry and style it.
If you want, you can use a box dye to cover the grey hair. You could also go to a stylist or barber to color your hair. This route would be best, so you get a perfect match to your natural color so you can go longer between coloring appointments.