Issues with going number 2’s

I'm hoping this might ring a bell with someone out there who may be able to offer some advice. DS is nearly 3 and has always been a bit funny about doing number twos. He will disappear, go and hide in his room for half an hour or more and if I go to check on him and open the door he freaks out and asks to be left alone because he's doing poos. I've even thought I'd lost him once, turned out he was hiding in his closet because one of my friends daughters was over and was playing in his room. I always ask him if he would like to go on the toilet instead, have tried encouraging him to do so but he gets scared and says no everytime... Is this just a phase he will eventually grow out of? If we're out he will hold on until we are home unless there is somewhere he can hide. He sometimes holds on for days to the point where he's so constipated and can't go because it hurts him so much and he becomes too scared and so tries to hold on even longer. This happened yesterday when he spent about 4 or 5 hours in his room and wouldn't let me near him, he says he's trying to do poos but will then say he doesn't want to because it will hurt him.

My nephew was the same, he used to hide when he was going poo's, he was TT for wee's, but flat out refused to use the toilet or potty for poo's and would hide under the table, behind the couch etc etc and not go for days at a time.
I dont have any advice, I think with them, he eventually just grew out of it.