Can I take my newborn out in public after it's been a week?
There is a difference between going outside and going out in public. Outside? Sure. Just bundle your baby in the same number of comfortable layers you wear in the weather, or buy a protective covering for the stroller that will shield your little one from a cool breeze or from precipitation. You'll go crazy staying indoors all day long, so it is probably good for your mental health to get out for a brief stroll around your neighborhood.
Taking your newborn to public places during cold and flu season is another story. In general, pediatricians usually suggest limiting contact with too many people in your baby's first four weeks of life--especially during the peak months of respiratory infections (spread by coughs and sneezes). While getting the common cold isn't horrible for a newborn, an automatic two-day hospitalization is necessary any time a baby less than 28 days of age spikes a fever of 100.4 F or greater. The stay will be full of unpleasant tests and IV antibiotics until it is a clear diagnosis that the baby just has a cold. This just isn't worth it! Worse, if a newborn does get the flu (and other respiratory illnesses like respiratory syncytial virus, or RSV) can get very sick.