Many people have difficulty digesting dairy and gas and bloating are some of the more common signs. There are two possibilities here: lactose intolerance or an allergy to dairy. If you are lactose intolerant the enzymes (Lactaid) should take care of the problem. If they do not, you may be allergic to dairy and all the Lactaid in the world will not make a difference. Do some experimenting; eliminate all dairy from your diet for a couple of weeks and see if the problem subsides. If it does, add dairy back into your diet and make sure to take the enzymes each time you ingest dairy. If the problem does not return this tells you that you need to supplement with enzymes each time that you eat/drink dairy. If you start having problems again while using the enzymes you are very likely allergic to dairy and will need to stay away from it - unless you don't mind the gas and bloating. By the way, an allergy is an immune response and puts a real strain on your body if you are frequently ingesting something that making you react. It is better to avoid it altogether.
You could also try switching to goats milk, cheeses, yogurts, etc, It is closer to human milk and often more easily digested by us two-leggeds.