Now that we've established what an intolerance is, let's start to look at what may be causing your problems. The best way to identify the offending foods is an elimination diet and food/symptom diary. You can find lots of free printable food diaries online. Here's one with a good explanation and example. Let's be real. An elimination diet is a simple, painless, non-invasive, FREE way to figure out what is making you feel like crud. There's no harm in trying it and seeing if it gives you some relief. If it does, you have your answer.
The first approach is a single food exclusion diet. If you already know that dairy makes you feel awful, then this is probably the place to begin. With a single food exclusion diet, you simply remove the food for four weeks. Keeping a symptom and food diary during this time can be particularly enlightening. The most important part is to make sure you are removing all traces of this ingredient for four weeks. You will need to read labels for everything you eat. (You wouldn't believe the number of foods that they add wheat and whey to.) If you slip up and have the offending ingredient, you will need to start over.
Once you have removed the suspect foods for four weeks, you can begin reintroducing them one at a time. Let's say the suspects are dairy and gluten. You have a clean record of a gluten and dairy free diet for four weeks and are ready to reintroduce. Do not sit down and have a piece of pizza because there are so many ingredients you won't be able to identify which one is problematic for you. You will still be following the "elimination diet" protocol, but eat one piece of bread or one cup of milk. Then, wait. Write down what you ate, when you ate it, and keep track of your symptoms for the next 48 hours. If you have no reaction, the food can be added back into your diet. Repeat until all foods have been reintroduced and you've identified the culprits.
The second option is a multi-food exclusion diet. In this case, you remove two or more foods that are the most likely culprits at the same time. The final approach is a oligoantigenic diet. This is sort of the last ditch approach if the first two didn't resolve symptoms. It's best to do this under the supervision of a healthcare professional because it is essentially a hypoallergenic diet. You're seriously limited in what you can eat and are at risk of malnourishment. Please contact a registered medical professional to discuss that option.