Hey Deos. Good for you for being cautious, but there's really no need in this scenario. Firstly, 10mg of Hydroxyzine (Vistaril, Atarax) is a relatively low dose, considering the dosage for anxiety relief and/or hypnosis generally begins at 25mg or 50mg. The main point is though, that Hydroxyzine is just an antihistamine. It's not a sedative/hypnotic like say, a Benzodiazepine. Benzodiazepines and Alcohol produce very similar effects in the body and a synergy is observed when the two are combined. This can lead to various complications like vomit aspiration or even death from respiratory depression.
Antihistamines will not contribute to this in any way. They have the ability to increase sedation, definitely, but not in a dangerous way. But, if Hydryoxyzine really affects you in such a major way, you probably should give yourself some time before consuming the alcohol, just because you probably don't want to end up fallin asleep.
High therapeutic index; no drug synergy or respiratory depression. You're good to go.