Haha, I thought I misread your message! Iirc, in the books it’s never clear, it’s never directly addressed, and the scene with Balon and Asha never happens, but I think it’s safe to assume that Theon suffered a similar fate:
(mild spoilers from ADwD)
He [Ramsay] has only taken toes and fingers and that other thing, when he might have had my tongue, or peeled the skin off my legs from heel to thigh. (ADwD)
Ramsay rose, the firelight shining on his face. “Reek, get over here. Get her ready for me.”
For a moment he did not understand. “I … do you mean … m’lord, I have no … I …”
“With your mouth,” Lord Ramsay said. (ADwD)
Those are the closest references to it that I can remember of. I understood Ramsay had him castrated as well.
Hi! I really wish I could help! But I’m afraid I have no advice of trick or anything like that (I’ve never been so sick after a night of drinking, but I have vomited until there were nothing in my stomach, and it’s a terrible feeling) :( You can try and see if your tummy can take a little of water with lemon (that helps me when I feel sick, but maybe you prefer tea, or chamomile tea), and don’t eat anything solid for some time. But if you really feel so bad, maybe you should see a doctor?