We have (had) this issue. The intestines in our family are nearly full size when we're born, and ARE full size by the time we're 2. Creates problems, because the exit is NOT full size! Ouch! Actually, giving birth was a comparable experience. It hurt a little LESS actually, to have my son.
So my son got that gene. In fact...there were days where I've spent over 2 hours holding and rocking a crying toddler...and there are days (maybe once every couple of months) where he still gets afraid...and has to be coached through it.
So it's been years.... of patience, and praise of his courage and, and encouraging his bravery. Which it is. How many adults are willing to go through something painful without trying to put it off? Not many I know.
The reason I've been willing to spend years teaching bravery? My mum fed us laxatives and shoved enemas into us until we were around 5 and she gave up...and I have to tell you...her being **angry** and Stressed Out over something that we had NO CONTROL (aka fear of pain) is probably my STRONGEST memory of my childhood. It doesn't matter how many pictures there are of her loving, and cuddling, and playing with us. Until I was 5 my mum was my own personal monster.
So be gentle.
Your son is afraid. Rightly so. After a few hundred or a few thousand times of something hurting...he's going to remember that it hurt. We usually only go through childbirth a few times...and never once a week, much less every few days.
It's going to take some time. With my son, it took until he was around 4. At about that age, he'd puff up his chest, put on his Big Boy face and tell me "Mum. I'm going to be very brave. I'm tough." and then march himself into the bathroom. And like I said...two years down the road at 6...it crops up once every few months.
If you wait until the issue is resolved, you may have to wait until they're 8 or 9...which...in talking with others in the same boat, is the age it generally "goes away". Our son was potty trained 100% by 3, but preferred his diaper for poops for another year. And then it was another 6 months before he didn't want me holding his hand in the bathroom.
So be gentle. And be his hero, instead of his monster.