I wanted to add a little more to this for anyone who might find it helpful. ^_^ (NOT a med student or physician, just a user! My experiences are also with using it specifically as a sleep aid, not for anxiety.)
For people who aren't familiar with hydroxyzine, it's similar to diphenhydramine (Benedryl) and doxylamine succinate (Unisom) in that it's an antihistamine with qualities that make it useful for other applications (all three have sedative effects, and diphenhydramine is also included in anti-nausea formulations such as Dramamine - there may be other uses as well; these are just what I know of personally, and I don't know that I've even seen doxylamine marketed as anything but a sleep aid (but again, I've never looked for it for any other purpose myself and someone else might be better able to comment on that)).
In the US it's a prescription medication (so I assume it's the same elsewhere). There are two slightly different formulations - hydroxyzine pamoate is branded as Vistaril, and hydroxyzine...hydrochloride, I think, is branded as Atarax.
I've been prescribed Vistaril for its sedative properties twice - the first on my request (at the time, I don't think I knew it was even used for anything beyond allergies; I just knew some people who took it and went flat so I was hoping it would do the same for me, and I figured since I do have allergies it might be something that wouldn't arouse suspicion), and the second when it was offered to me as a "replacement" for Ativan/lorazepam at the clinic I had to start going to after I moved, which considered Ativan a strictly psychiatric drug and would not prescribe it for me as a sleep aid - I would have had to enroll in their behavioural health program (and was pressured to do so as a show of "good faith", which eventually caused me to have a PTSD-triggered breakdown in the office when a new practitioner ignored my accomodation plan, Rule #1 of which is do not continue pushing after I've said no), which I refused because I've been through that hell before and I'm not voluntarily subjecting myself to more. I've since been able to switch to a provider who doesn't have those restrictions, but I've continued to take the Vistaril along with the Ativan because:
I have the tolerance of a Tyrannosaurus, and neither of them do crap for me on their own (they don't even really do crap for me together, so I'm actually still supplementing them with additional meds). But if I could only take one and had the choice of which, it would be the Ativan, no question (I realize the OP asked because they already know they can't get benzos; this is more for people who have options but are considering what they should go with). Obviously my tolerance for everything has increased because I've been taking them for so long, but even when they were new to me, or if I've had one of the rare but much-loved periods where I don't do anything BUT sleep for a few days, don't need them, and get slightly "reset", Vistaril has never had the kind of effect on me that I hoped for (the Ativan sometimes becomes temporarily more effective again after a break, sometimes not). My ex has a prescription for Atarax, but also numerous other meds for both physical and mental conditions (he had Seroquel at one point, not sure if he's still on it, but he offered some to me then and I ran away screaming because of the horrible expeiences I've had with psych meds - I guess if you're using them to help CTB it doesn't matter, but we were just trying to get me some sleep, so my response was nope nope NOPE), so when he DOES sleep it's not always clear what actually did the helping unless he only took specific things, and there are many, many days that nothing works for him as well (though I can say that despite him being much heavier than me, when he does feel the effects, it's sooner and more strongly than I ever do - we've had debates about how long it "should" take things to kick in and why don't I take them on that timeframe like I'm "supposed" to). I did once hear someone comment that her husband was a zombie with 25mg of Vistaril, and I laughed and then cried because my starting dose was twice that and...yeah.
Granted, any medication is a crapshoot as to whether to it'll work for any given individual or how well, but my experience with hydroxyzine is that it has zero effect on my anxiety (as mentioned I don't take it for that purpose, but I fairly often have panic attacks when I go to bed because of how hard it is just to go to sleep, and there's no difference in how severe they are with or without it), has limited effect on my ability to sleep (whether that's going to, going back to, or staying once I'm there), and if I was at the bus station, can't imagine it helping me get on board by itself. I would probably still take it, but do so along with anything/everything else I was planning to take in the same way I do now - hoping it might support, but definitely not relying wholly on it - unless I had something that was so much better than the others combined that it alone would be enough.