This does sound very much like lactose intolerance however you could have a dairy allergy. You should go to the Dr and have that checked. For now avoid dairy if it is causing you so much trouble. The one thing to remeber is Lactose is in more then just dairy for example many store bought speggetti sauces have it , as does milk chocolate. Here these links might provide some help. I have copied some information as well below.
Milk allergy Vs. Lactose intolerance
Some products labeled nondairy, such as powdered coffee creamer and whipped toppings, may also include ingredients that are derived from milk and therefore contain lactose.
Smart shoppers learn to read food labels with care, looking not only for milk and lactose among the contents but also for such words as whey, curds, milk by-products, dry milk solids, and nonfat dry milk powder. If any of these are listed on a label, the item contains lactose.
In addition, lactose is used as the base for more than 20 percent of prescription drugs and about 6 percent of over-the-counter medicines. Many types of birth control pills, for example, contain lactose, as do some tablets for stomach acid and gas. However, these products typically affect only people with severe lactose intolerance.