Elimination diet requires cutting out all forms of dairy for 6-8 weeks and paying attention to see if any of your symptoms (sleep, digestion, nasal congestion, anxiety etc) improve. At the end of the elimination diet you reintroduce dairy and see if you notice any of these symptoms reappear. It is often hard to notice the symptoms improving because it is a slow process (much like CPAP) but you will notice the effects more when you try to reintroduce it. In my case it was hard to pinpoint because the majority of my symptoms do not occur directly after ingesting dairy but rather 1-3 days later, because of this I had to try eliminating and reintroducing a few times to make sure it was the cause. If you reintroduce and think it may have had an effect but aren't quite sure cut out dairy for another couple weeks and try reintroducing agian. I had to do this a few times but eventually it became obvious when I realized the majority of my symptoms appear 2 days later.
Eliminating dairy is a bit of a pain but not that hard to do especially for a short time, there are lots of alternatives like oat milk, almond milk, soy milk, plant based cheese etc (I am far from vegan but they are a great source of dairy free food). The biggest pain is how many processed foods have thinks like modified milk ingredients or the odd restaurants that have poor dairy free selection.
If you find you do have a reaction to cows milk then it is up to you if you want to remove it from diet completely or if you want to try reintroducing lactose free dairy products. My recommendation is to avoid these during first elimination diet because many people are intolerant to the protein (casein) rather than lactose so remove both at first and then test lactose later.
Dairy intolerance is common and can have a huge impact on a persons health, unfortunately there are no tests for it other than elimination diets.
Edit: Here is a link on the topic, aimed at children but applies to adults as well. You can find many other similar sources but need to differentiate between allergy and intolerance.
https://www.urmc.rochester.edu/childrens...rance.aspx
"Cow’s milk protein intolerance (CMPI) is an abnormal response by the body's immune system to a protein found in cow's milk, which causes injury to the stomach and intestines. Cow's milk protein intolerance is not lactose intolerance."
"In IgE-mediated CMPI, symptoms can start within 2 hours of drinking cow milk, whereas in non-IgE-mediated CMPI, symptoms can happen from 2 days to 1 week after ingestion of cow's milk."
"The signs might manifest as a skin rash or eczema, or involve the GI tract, such as vomiting, abdominal pain, blood in the stool, mucousy stool, and diarrhea. Prolonged issues in infants could lead to wheezing, irritability and poor growth / failure to thrive."
"The diagnosis of CMPI is also supported by an improvement in symptoms after the elimination of cow's milk. Most of the time, blood tests and other invasive studies are not helpful."
I think this is potentially what happened to me. I had a known dairy intolerance as a baby that I was believed to have grown out of. I think 3 decades of dairy consumption damaged my digestive system. This can cause all sorts of issues as our gut is heavily involved in neurotransmitter synthesis, immune system, nutrient levels and more.