It seems to be standard advice to blow your nose when congested from a cold, but is there any evidence that this actually helps, either with severity or duration of symptoms?
In my experience keeping your nose blown (or even rinsed out) prevents a secondary infection in your throat. Whatever you don't blow out of your nose dribbles down the back of your throat and bacteria get happy there and give you a sore throat. This is technically a different second infection but most people will treat it as a single long cold that "moved down" as it progressed.
There was a study that suggested nose blowing would put mucus and bacteria up into the sinuses and result in a secondary infection there, but all the nose blowing was done by people lying on their backs, which doesn't seem super representative. To be on the safe side, blow as gently as possible, and keep in mind your own tendency to get a sore throat after a cold or to get a sinus infection after a cold.