For a possible diangosis of some form of acid reflux, why would an antihistamine such as hydroxyzine hcl be rx'ed?

Not option 1 or 2: One of the 1st choices often used are a class of medications that block a specific histamine receptor found in the stomach (H2, end in -itidine or -otidine, for example). Hydroxyzine is a non specific histamine receptor blocker, so it will work in the stomach as well as other places. But it is rarely used for this reason because of its other affects. There must be something specific to this case.

Acid reflux: Symptoms of acid reflux can be from GERD, allergic rhinitis (the reason for treatment trials of antihistamine), or asthma. Your doctor likely felt from what you described that your symptoms may benefit from this medication. If no improvement, just let your doctor know and you can work on figuring out if the other causes are contributing