Not much to do
Not much to do to help babies at this age.
Antibiotics do not kill viral colds and will not help. Cold medications are not approved for use at this age either. You can try nasal saline and bulb suctioning to get the snot out. I find that sitting in a hot, steamy shower (the water should not touch the baby - just sit in the steam) with the baby upright to get the snot to flow out, will help.