*whispers* Jed's a doctor. Jed would help if John asked though he'd have some man pain about it.
If we’re talking about Apollo!John, he wouldn’t have asked.
His training has made him solely rely on Diana (and therefore The Founder, who may have had a hunch of what Roger and Jed were planning and pushed John as far away from them as possible-- while Roger, to note, is still alive and AWOL from Ultra.)
While, sure, he needed a doctor for Diana, the first thought across his mind was expediating, not sending a message to get Jed. Which was 100% part of his conditioning in the Apollo program.
In the Ultra Forever verse (to give you some potential man pain), he is still very close with Jed, but also not even bothering to hide he is dating Stephanie (who basically, after Roger died, turned back up and Jed sent John specifically to recruit her. No bag over the head nonsense tbh). I feel like this is the ‘what would have happened’ if Killian had been the one to kill Roger (as per the original plan), and John only went through the Anax project to take Killian out or bring him to heel (and drop him in a Citadel cell, because I really think Killian would have gone off a bender [Rook’s playing him as dual identity: ‘Ian’ and Killian to deal with the project] regardless). Basically, John is becoming more like Jed, take it or leave it. And he’s a little more domineering (probably a trait learned from Jed)