The internet does poorly with sarcasm so endulge me in clarifying that applying pressure on the wound isn't for revenge; that's what you're supposed to do with bleeding and head injuries. The pressure can take away some of the sharp pain but more importantly, it tries to keep the blood from flowing out of the body. If it were a limb, you would try a tourniquet.
The ideal situation would have been to keep the knife in because it blocks the flow of blood the best since it was the one to make the hole in the first place. It's all about increasing the amount of time you have before you can reach medical care.
I don't know if it is the same in Korea but in the USA, when someone undergoes surgery with blood loss, the family is asked to donate blood if they can. That could be a potential baby reveal (though they look at cell count instead of hormones and if Euihyun is underweight, they won't take blood from him.)
Yes you're right about applying pressure to the wound, that's a fact for sure. But what I meant about "for revenge" is Euihyun was already pressing on Taejus wound then the secretary told Euihyun to press harder thus applying more pressure and Taejus getting angry because, obviously, it hurts and he can't show that he's angry because Euihyun is the one that's doing it.
It's really not that important, it was just a playful part shown because of all that's happening, like the author just put a silly little part that readers can chuckle to.
Taeju is hurt real bad, Euihyun was told by the secretary to press the wound real hard (the secretary's revenge because he was dragged to fight, it's funny I swear), they rushed to the hospital (wishing they check on Euihyun too so they would realize that he's pregnant) , while in the car Euihyun said that he will forgive Taeju if he doesn't die because of his injury (crying Euihyun will be the death of me), last panel showed Euihyun sitting in the waiting area with bloody hands.