Turning into a completely different gender is not a common occurrence. People tend to explain stuff away and being "sick" is no different. Any symptoms of something wrong with his body he found an excuse for "overwork", "insomnia", "stress", ect. Gi-Hyeon really didn't have any reason to believe that he had turned into a completely new gender without his knowledge. And though it's not really shown so much in the webcomic, he actually DID end up getting blood drawn at the clinic right before he nearly got hit by the car. So he would have found out about his new gender and pregnancy anyway. As for whether or not Yeon-oh would have known or found out is dependant on the privacy laws.
i agree with what u said(same thoughts) & i get that secondary gender conversation is an absolute rarity. but if i had leakage from my 'behind' twice, feeling warm for no reason, being able to scent, AND have 2-3 random pple mistaking me for an omega, hell i'll start thinking about the impossible happening and demand a rushjob on that bloodwork. maybe that phrase 'doctors makes the worse patients' applies to Gi-hyeon too(healthcare prefessional)
Doctors absolutely DO make the worst patients. But in defense of anybody. (omegaverse or otherwise) I think the absolute last thing to ever cross my mind would be "my literal biology changed". But I also would be looking for a rush on the bloodwork. He hadn't gotten it done too long ago in the story before he found out though. If I remember the timeline of the story correctly, he gets the bloodwork done right before they break up, and I think the (almost) car accident is either that night or the next night. So it was less than a day.

Lol and it's been months since he turned omega so if he were rlly keeping track on his health and he built that hospital for him then he should've got a report already that he manifested gosh