Decades ago, I worked as a milk man delivering this superior product. It does taste better.
Almost all milk is pasteurized, so it will have a decent shelf life if stored properly. Check the temperature of your refrigerator, I think 36 or 37 is the right temperature and store it towards the back.
As an aside - milk processing is counter intuitive. All of the fat is removed and then skim milk is bottled. Then they start putting the fat back in and homogenizing to make 1%, 2% and whole(3.25%?)