Hi, Welcome to HealthcareMagic Forum.
Your one month old kid has a Upper Respiratory Tract
Infection (URTI), May be Viral, that is common cold
. It is in the initial stage and he may develop fever
later. You should be taking him to a Pediatrician
so that he can evaluate him completely and rule out the exact cause. Get a Chest X ray
if necessary after discussing it with his Doctor. He will require antibiotics and nasal decongestants if the congestion is severe. It will go away in a week or two, give him fluids and continue breast feeding if you do and Practice Good Hygiene at home.
I Wish him Good Health, Take Care.