"Hives" is sometimes used as a sort of abbreviation for "hyperventilation", thus someone "getting the hives" when doing something specific could mean that he/she is so very excited by doing it that it causes him/her to hyperventilate.
Hyperventilation can more often be observed in children or people who tend to react a bit child-like (just to these specific things). Nevertheless, using the expression "hives" doesn't necessarily mean that they *actually* hyperventilate, only that they're overly excited.
OMG! I was just able to get my hands on one of those spectacular new '60s-styled klogs! *hives*
Oh, don't be too bothered by all the enthusiasm. Frances always gets the hives when she has the opportunity to spend some time with the horses.