I agree with GuitarRox - yes, in theory you could get it this way, but in the absence of a cold sore, it's not that likely.
However, you could easily get a cold, strep, the flu, etc., this way, and it's the season for it, so let people get their own drinks from now on. :)
Oral herpes or herpes simplex one is extremely common and a huge percentage of the population has it. Young kids have it. It's pretty straight forward . . . cold sores. Some people get tingling before an outbreak. But the jaw hurting and all of that is not herpes. Can you get herpes from sharing a drink? Theoretically and occasionally but I would not be overly worried about this.