Hi OP,
In my experience, the reaction to dairy can change with age.
My eldest was diagnosed at a very young age as dairy intolerant. He was breastfed at the time, and at 3 days of age the screaming started
thankfully a midwife friend suggested giving up dairy, and the screaming stopped. I continued to breastfeed and supplemented with Nutramigen.
Unfortunately we received pretty cruddy advice from a paediatrician (who DS later saw for reflux), and we were told to periodically trial him on dairy to see if he had outgrown the intolerance 
Initially, at about 9 mo of age, he seemed to tolerate dairy - but after some weeks of having dairy (yoghurt) daily, I noticed he was becoming increasingly constipated. I stopped the dairy for a while, and his constipation resolved. When I retried it a few months later, the constipation returned, this time accompanied by a nappy rash.
I know it will probably be difficult (my 25 month old hasn't had yoghurt for at least 6 months, but still remembers it and asks for it), but could you try cutting out dairy for a couple of weeks and see if the constipation improves? It may at least give you something (else) to tell the consultant when you are seen in clinic, irrespective of the result you get, and may save you time, in terms of getting things sorted for your little man.