I was under the impression that diarrhea, not constipation, was the major symptom of Crohn's and the other IBDs.
Do other dairy products bother you? Have you tried laying off them to see if your constipation gets better or worse? Dairy is a trigger for some people, but not for all of us. My recommendation, if you haven't tried it already, is to not eat any dairy products for two weeks and see if your guts get any better. Then add a daily dose of dairy back into your diet for a week and see if anything changes. If not, then you may want to try a week with two doses of dairy daily and see if that does anything. I figure if it doesn't make you worse, why not eat it? If you do find that it makes you worse, then only you will know whether cheese is worth 1/2 an hour on the pot and a sore bumhole. Sometimes all of us trade off health for something we really love to eat, but for the most part we abstain in order to feel better.