Hi there,
Our daughter has suffered a lot from constipation. She's three now.
When she was younger we tried all of the tricks: fruit, juice, limiting certain foods, everything that other mommies have suggested so far. Nothing worked. We always offered her water but she was never interested and didn't take enough liquids.
We went to a specialist who suggested that we cut out dairy, but otherwise keep all other foods in her diet. He said the foods that others suggested eliminating from her diet were not the problem. He said her dairy allergy was causing her pain when she passed stools (he said her little anus was very red and irritated, but I didn't know he difference, had never looked at anyone there before!), and that pain caused her to hold her stools. This created a horrible cycle of holding the stools, making them harder, causing passing of them more painful.
Anyway, I'd suggest cutting out the dairy for a while (I think it was a few weeks) to see if that helps. It would be worth it to find the cause at this point before the problem escalates. Constipation can be so awful for little ones and can take a long time to get over! If it doesn't clear up soon, whatever you decide to try, take your little one to a specialist instead of waiting. I don't mean to be alarming, I just wish we'd done so sooner. Our daughter really suffered.
Good luck!