You poor thing. Your poor son. Did your dr tell you that it's common for 2yr olds to sometimes hold their poop for no reason? Toddlers sometimes do that when they become aware of their body & can also come about during potty training. Kind of a control thing, meaning they can feel it coming & dont really know if they like what's happening sort of thing. It's just body awareness.
So he has a irritation on his bottom & the dr. thinks that by making him poop more that will help? I wonder if you & I share the same ped practice (I'm looking for a new one). Just from what you've shared here, seems to me that your son is telling everyone that it hurts when he poops because he already has an irritated bottom, not that he's constipated. Has the dr. been able to determine what the irritation is? I assume that at 2yrs old you son is probably still in diapers? I wonder if he has a yeast infection, aka full blown diaper rash, or even some kind of dermatitis.
If it were one of my kids (& believe me, we've been thru the medical ringer with both our daughters, unfortunately) I would just trust my gut. I've found that every time I went against my mother's intuition & followed the dr's advice, I regret my decision later.
If you are still having issues with his sore bottom, have you maybe considered going to a natural food store or even natural food co-op to find a natural, topical cream that is non-steroidal & non-petroleum based? Titanium oxide or zinc oxide are ingredients you want to have. It makes the white paste that gets messy, but it offers a protective barrier from urine & poop, so it wont sting or not sting as bad when he goes. Anything with mineral oil/petroleum/petrolatum will only slow the healing process because it wont allow his skin to breath.
And if you find that the irritation keeps coming back, you might want to consider "pro-biotics". You can get a chewable tablet, tasty little thing, that gives kids age 2+ all the healthy bacteria for their intestinal tract. That will also directly help with stomach irritations, constipation, loose stools & is a general immune booster. NO side effects, you cant overdose on it, it doesnt react with other vitamins (not like taking too much iron or anything like that). I've had both my kids on probiotics since they were infants (they have infant versions) & it's the only thing that has kept them virtually gas free, constipation free, stomach ache free - they both have food allergies.
So sorry to be so long winded here! I empathize with your frustration & I hope this helps! If you have any other questions, you can email me at ____@____.com