I'm surprised your doctor didn't catch this. One website I visited warned against taking any narcotics, including Vicodin, while on vistaril.
Your doctor should know whether or not the pills will interact. If you are seeing several different doctors, they should each know ALL of your medications. If you are planning to take someone else's medicine, that is never a good idea. Doing that could cause a dangerous drug interaction.

Also, use only one pharmacy because it's their job to catch it if the doctor missed it or if you are seeing more than one doctor.

Thanks for adding that, MyrahU. It's always a good idea to use only one pharmacist as well.