A seven days old baby generally has nasal blockage rather than running
nose. However it is not uncommon to have nasal discharge due to common cold
. If the discharge is watery and there is excessive sneezing then it is a viral flu
like infection and the baby recovers after a few days without any medicine. However if a thick yellowish or greenish discharge comes out especially when the baby sneezes, it is suggestive of a bacterial infection
which needs to be treated with appropriate antibiotics to be advised by your pediatrician
. So best will be to consult your pediatrician. Any infection seemingly mild in a newborn baby should not be ignored and timely treatment must be sought without delay.
Get the BCG vaccination as soon as possible but it won't cure or protect the baby against cold as BCG is for prevention against TB only.