A "sip" is a small amount of a drink. It's less than one mouthful.
When you're asking to drink someone else's drink, it's common to ask for "a sip". That's because you don't want the person to think that you're going to drink a lot of their drink!
If you want to talk about drinking a large amount of a drink all at once, use the word "gulp". It means a full, large mouthful of a drink.
To describe swallowing a medium amount of a liquid, call it "a mouthful" or "a swallow":
Hey, give me a swallow of that.