I recommend getting tested. With dairy, it could be lactose or casein or both.

gluten intolerance could be Celiac disease, which is a serious autoimmune disease. If it's celiac, it's important to have a correct diagnosis, as gluten doesn't just hurt the gut, it also causes irreparable damage to other organs. A diagnosis of celiac requires a biopsy of the intestines to see if the villi are damaged. For that, she still needs to be consuming gluten. If you stop gluten and the gut starts healing, a biopsy won't find anything. I stopped gluten before getting tested and so I can't get a correct diagnosis. This means I occasionally consume gluten and I don't know what kind of damage I'm doing to myself.

For the gluten intolerant, consumption can also affect brain activity, behaviour problems, moods, fatigue as well as other issues. I'm not familiar with problems from dairy. I've only just stopped dairy for DS3's sake.

i highly recommend getting a referral to an allergy doctor, although you may need to wait months to see one. A GP can refer to testing as well.