Personal fanon regarding nu!James T. Kirk and Starfleet Medical.
1. In Star Trek, the 'bubble universes reproduce through black holes' theory of the multiverse is true. Which makes the Nerada and the Jellyfish to have traveled through a black hole into a white hole, rather than a wormhole. Wormholes are a black hole/white hole pair in the same universe. What Prime did was go through a black hole and bud off a new baby universe. In a faintly geeky way, this makes Spock nu!Trekverse's parent, since he created the black hole.
2. Jim was born approximately two month premature. It was the random particles emitted from the white hole that sent Winona into premature labour - however, part of this was the multiverse making sure storylines stay on target, as anything was pretty much possible to cause premature labour in Winona. She managed it back in Prime by tripping over a pig in Iowa, for sakes. High concentrations of odd particles was certainly enough to set her off.
3. Until Jim was born on Medical Shuttle 37, humidicribs and the instructions on how to retrofit equipment to build one were not standard procedure in Star Fleet. After Winona the Engineer had to jury rig one with the assistance of the medical techs and doctors present shortly after giving birth, instruction booklets on multipurposing equipment became standard procedure. Winona used some of the good will from George's death to ram that through the Admiralty, since she didn't want any other parent to be told by doctors that they might lose their new baby due to a lack of basic equipment.
4. Yeah, the space rays gave Jim allergies, since he was born very preemie. He also almost died on that shuttle, until Winona got that humidicrib built.
5. The only thing that kept Jim alive until they could stabilise him in a protected environment was the Betazoid doctor who telepathically bonded with baby Jim and kept his heart beating and his lungs breathing. The contact enhanced Jim's empathic abilities.
6. Until Jim left home, he'd never seen a non-'Fleet doctor. One of the doctors who kept him alive ended up working at Fleet Medical near the Academy, and dealt with all of Jim's childhood medical needs and yearly physicals. The first time Bones saw Jim's unexpurged medical record, he nearly had a heart attack over the amount of classified information in it. Then he had another one over its completeness, and Jim's involvement in several medical studies, and a third when he realised Jim was "Case Study Baby T".
7. It took the Vulcan Science Academy 2 years and dozens of academic papers to create Spock. What Jim never tells anyone is that his birth was the source of at least a dozen medical academic papers as well. He's involved in a long running study on all children born in low-shielded conditions, and on three different allergy studies (space rays give allergies, allergies resulting from consumption of blighted grain and general rare allergies and their manifestation). Some of the current medical courses at Star Fleet use "Baby T" as an example in class.
8. Fleet Medical have a stash of lollies they use to bribe Fleetbrats when admitted. Jim was one of the only cadets who still received treats from that stash when he ended up in Emergency.
9. Half the nurses and doctors in Emergency at Fleet Medical already knew Jim prior to his joining Star Fleet. The first time Bones hauled him into Emergency after a particularly bad barfight compounded with an allergic reaction, McCoy was shocked to see the nurse at the desk page one of the senior doctors at the sight of Jim and start him on a non-intuitive antihistamine. By the start of Second Year, the rest of the regular staff in Emergency knew Jim too.
10. After Tarsus IV, Jim ended up an inpatient at Fleet Medical for several months, until he'd reestablished healthy eating patterns, figured out what his brand spanking extra new allergies from eating blighted grain were, and put on enough weight. Memories of this among staff in no way caused point 8 to happen when Jim became a cadet.
Yes, I'm aware there's practically a story here, but I don't want to write it.