Cow milk before age one

Update: For all of you asking, we have tried every single possible food and drink that is said to help with constipation. He's gone through more doctor appointments than I can count with a new suggestion each time. The GI specialist wouldn't see him until his pediatrician tried every tip and trick in the book. Our oldest had some slight issues as a baby as well so we already knew about the 6 P's and the juices to help. Things have gotten worse for him in the last few weeks and we are looking hard and wide for a new GI specialist to take him to. We did not go the milk route, due to the increase in his problems lately.

I'm running out of options for my 10 month old. He has had severe constipation since he was one month old. We've gone through hoops with his pediatrician and the pediatric GI specialist. They insist on continuing to give him copious amounts of medicine to help. Problem is they don't help at all! He's on nutramigen for his formula and gets lactalose and enemas. His bowel movements are so hard he rips and bleeds with every bowel movement. He will be miserable and in pain for 2 to 3 days before he can even get anything out. It seems to me though, that whole fat yogurts and milk mixed in oatmeal help him get things moving a bit easier. Has anyone given milk in a cup before a year and had success? I'm not trying to replace his formula, but to supplement a bit. Obviously since I'm in the US, it's recommended that we wait till he's a year old.