My DD had that when she was around 2 as well. Apparently it's pretty common when they're around toilet training age - they learn that they CAN hold it, and so they DO. And then it starts to hurt, and so they don't want to go, and it gets worse.
Anyways, I found that mixing 1/3 apple juice, 1/3 water, and 1/3 prune juice worked really well. If I didn't add the apple juice, she wouldn't drink it. She didn't like the taste of prune juice.
And, for what it's worth, the constipation issue continued off and on for a number of months with my daughter, but it did totally clear up, and now she's normal.
All the best!