We're going through the same thing with our 21 month old. She got constipated and now clinches so she doesn't poop. We've had to resort to physically forcing her if we can tell she's tensing. We either hold her back to our stomach and pull her knees into her tummy (like she's squatting - or giving birth) or lay her on the ground and pull her knees into her tummy.
We've been giving her SO much fiber, but it's not helping.
I had severe constipation during chemo which gave me awful hemorrhoids (I used to be embarrassed to talk about this, but not now after 2 kids and cancer).....I still take Senna every day (natural vegetable laxative and stool softener).
I'd recommend calling your pediatrician. Most are going to recommend Miralax. It is expensive, but it's a great previous Rx now over the counter product. A pharmacist also suggested a laxative (Pedialax) which did help.
Giving her more fruits and veggis will help as fiber will make the consistency easier to pass and make her go better. You can also try any FiberOne product as they have TONS of fiber, but I'd ask your pediatrician to make sure there aren't limits on how much they should have in one day.
Good luck. We're right here with you.