Did you know early in the relationship that he had had the vasectomy - as in, a clear statement that he never wanted children? Were you listening?
Or was that a much later revelation that he initially kept a secret? Was he telling you the truth?
The difference is important.
Whichever, he's told you and told you and told you for a while now that he doesn't want to.
With an adult SD in the mix, I wonder if he is older than you are?
The prospect of later fatherhood can be daunting. The energy levels alone can be a challenge.
I wonder if the whole pregnancy, childbirth, baby thing grosses him out hence taking steps young to ensure it never happens for him?
He says he has a concern about your spinal health - he might be terrified of what he's projecting that might do to you, even leave him raising a child alone - but that might well be a handy excuse he's latched on to. Something he can cling to, even tho the consultant has reassured you.
He has the right not to want children and to stick to his boundaries.
Just as you have the right to want.
Neither wish trumps the other, neither should have to give in.
So your choice is
Stay together, and never have children, living with regret and resentment.
(And never forget how often we hear of women who resign themselves to staying childless for a man who didn't want them - only for him to bugger off with a younger woman when she hits her 40s and bingo there's a baby for him.)
Stay together and do the getting pregnant some other way, maybe in secret, knowing he doesn't want this - and risk his regret and resentment and a poor child who wasn't wanted by his legal father.
(Don't assume he'll fall in love with a fait accompli baby.)
Stay together and explore fostering (which takes a very special set of skills) or adopting - bearing in mind if he's clearly not enthusiastic you may not be found suitable.
Agree that you just want different things and go your separate ways, hoping that you will be able to conceive and carry safely and that your consultant was right.
All the best to you both whatever you decide. But you have to be having the hard conversations, not the arguments, now.