My DS rarely pooed as a newborn, I was told that was because he was fully BF and a huge 10 pounder, so there was no wastage!
By the time he was 3, he was regularly complaining of tummy pain, had swollen tummy like your photos. Was crying in pain, unable to eat or drink etcAnd regularly vomited (because there was nowhere else for it to go)
He was refered to the "pace team" at local hospital, who explained that because his bowels had not been moving things along as they should, they were bag/sack shaped rather than tubular. The blockages had to be cleared then maintained before the bowels would be able to shrink back into shape.
He has been on a movical and picosulfate regime. Movical is NOT a laxative, it works in a similar way to the gell stuff in babies nappies by absorbing water and softening the poo. It's therefore important that the child drinks plenty. Dehydration is biggest cause of constipation. The pica sulphate is a laxative however.
It's been complete trial and error to work out dosages for both. You can't solve the problem overnight. my DS is now nearly 7! He is doing ok. His biggest issue is not drinking enough at school and their unwillingness to support me with this. (But that's for another thread) he still takes movical daily but very rarely needs the picosulfate. he finally has an appointment with a dietician as I suspect wheat is a problem.
It really is a long slow slog!
I would pester your GP again, to get an "urgent" meeting with the consultant. I hope the poor little mite is better soon!