I always find it so absolutely hilarious that the first thing people automatically say when a person complains about dairy products is, you must be lactose intolerant (meaning your body can't digest the sugars in cow milk).
A person can become ALLERGIC to either the casein or the whey protein in cow milk at ANY time in his or her life; you don't have to just be a baby or a small child to develop the allergy.
If you have lactose intolerance, you can take an over-the-counter pill that will allow your body to digest the sugars so that you can continue to still eat and drink cow milk products. However, if your lactose intolerance is severe, even that might not cure all of your problems.
If you have an allergy to either casein or whey protein in cow milk, then the only way to stay away from being sick, feeling bloated, having diarrhea or constipation, or any of a myriad of other issues a person can have from an allergy is--you have to STOP eating ALL cow milk products. Period.
Taking probiotics is absolutely wonderful and is a great way to put good bacteria into your colon/gut, whether you have an issue with dairy or not. I take one every morning and every night, as does my daughter.
However, IF you have a cow milk ALLERGY and you don't quit eating cow dairy products, you can develop a LEAKY GUT, which will break down the barrier between the gut and your body and allow nutrients and other bad stuff to "leak" out of your gut and into your body, where they can cause further damage, not the least that your body will lose vital nutrients, vitamins, minerals, enzymes, and amino acids it needs to properly function. If you continue to eat cow dairy products for years and years and years--even though you shouldn't, because you are allergic to them--then your body will be an easy target to develop other food allergies and other food intolerances.
If you're having issues with dairy, I urge you to go to a doctor and find out for sure if you are ALLERGIC to cow dairy products or if you have LACTOSE INTOLERANCE. Either way, staying away as much as possible from eating anything with cow dairy in it will be the best thing you can do for your body.