Is he pregnant again? But they just did it yesterday (in the manhwa timeline).. or maybe he threw up because his body is rejecting that other alpha..
In omegaverse, once you've bonded with someone aka got bitten you can't have sex with other ppl anymore. Your body will reject what you're doing and will show clear signs of it i.e., hyesung feeling sick and dizzy then eventually throwing up.
so yes it's the latter
She's making me reconsider my gender..