I'm not sure whether constipation is associated with lactose intolerance. I have lactose intolerance and I certainly don't get constipated ;) I'm not as sensitive as you, as I can eat small amounts of lactose. If I eat too much lactose I get bloating, cramps, gas and diarrhea.
Have you tried lactose-free milk? No lactose...only dairy. See how you react to that. Just don't buy Wal*Mart brand...I think they skimp on removing the lactose and leave some in the milk! LOL.
After 3 years of chronic digestive disorders my symptoms turned into skin rashes, and then onto a more serious one - sinusitis. I suffered from killer sinus headaches for 8 months (not even thinking it was related) when finally my doctor did some blood tests which discovered that I am lactose intolerant as well as allergic to dairy (and eggs too). The test showed that eggs were off the chart and milk was right under. I have never really been a big fan of eggs, only an occasional piece of cake or biscotti here and there - I was more into cheese and never drank milk. I was only eating eggs in really small amounts. So, after one month of no eggs or dairy whatsoever (to be on the safe side) my sinus headaches began to go away. (Of course the doctor didn't think or advise me that it was directly related to my allergy). Now, after about 6 months of not eating eggs I made a stupid choice out of cravings and had a waffle and then some french toast a week later, my sinus headache came back with a vengeance. One week after no egg/no dairy my head is finally feeling back to normal. What a total drag. I absolutely hate this. I sympathize with you, but I would suggest getting bloodwork and a holistic doctor to help you out.