It is generally better to let your nose run when you have a cold, as blowing your nose too forcefully can cause irritation and further inflame the nasal passages.
Blowing your nose gently, however, can help to clear the nasal passages and remove mucus, which can make breathing easier. Clearing the nasal passages can also help to reduce the risk of developing sinus infections, which can occur when mucus gets trapped in the sinuses.
It’s also a good idea to use a saline nasal spray or drops to help moisten the nasal passages and make it easier to blow your nose. Drinking plenty of fluids and using a humidifier can also help to thin out mucus and make it easier to clear.
If you’re experiencing thick or discolored mucus, it’s good to consult with your doctor as it could be a sign of a bacterial infection and may require antibiotics.