It would actually help to know where in the world you are located, I understand if you don't really want to share but countries differ significantly in what medications are actually available. I assumed you were in the UK since you mentioned pregabalin specifically, re-reading your post I'm not so sure but I wrote the below prior to reconsidering, maybe it'd still be helpful to someone.
The UK NICE prescription guidelines are an absolute archaic upside-down mishmash of nonsense which hasn't been updated since the 70s or 80s but pregabalin somehow snuck in there by virtue of just being in the right place at the right time, I forget the exact reasons for why or how that happened, despite the UK's culture of complete and irrational fear of any benzo except diazepam which'll almost never be prescribed for mental health reasons, and arguably isn't the best one for it anyway, and the complete absence of the pharmacopeia of other newer, arguably more useful benzos that are prescribed in less culturally backwards dumbass countries like ours with more advanced medical systems and more evolved cultures generally, like the better parts of Europe.
Anyway so [if you are in the UK] pregabalin is still very much an option and on the list of options for Generalized Anxiety Disorder specifically, IIRC, but you do very much just have to jump through the fucking hoops. Insist on being referred for talk therapy, if you haven't had it before you should do that anyway, it's a waiting list but actually not too bad and the first thing will be basic CBT which if you haven't tried it you probably should try it even though it's pretty basic and not that helpful for many people, don't let me nocebo you though, please. If you can tolerate it at all just try to take an SSRI for a while like they want you to, if side effects become intolerable stop taking it, ovbiously, tell them that, they'll want to put you on another. You can just refuse at that point if you want but usually the practice is try at least 2 SSRIs, maybe an SNRI then look at other options. You do not have to do any of this, you really do just need to badger them and persist, but a GP can't prescribe pregabalin so you'll need to be referred to an actual psychiatrist which you must just insist on, do not take no for an answer, generally I think this might have to happen via the initial NHS Talking Therapy services, you'll have to have at least one assessment appointment, after that you have more chance of being prescribed something actually useful. I haven't done this personally (yet - actually I'm not sure pregabalin is suited for me for various reasons - it's not off the cards) I've just done a lot of research and have a lot of experience battling NHS bureaucracy, generally. It sucks obviously because you need to be in a certain state of mind to be able to even advocate for yourself and this is very much by design... certain people in government would like people with mental health issues to just shut up and go away and die, basically.
...OK so I just edited my opening sentences realizing you might not be in the UK. Even if you aren't the advice above may still be somewhat applicable but you really need to look into the typical prescribing guidelines for your country for mental health indications to see what's available or even legal to offer. Also, you said you went to see a psychiatrist, I notice - not just a GP type doctor - did you do this privately? If so (or even, potentially, if not) - you can potentially just try another. You didn't do anything wrong mentioning other medications, in a vacuum, but in practice it depends who you're talking to and while some medical professionals will be open minded to their patients wanting to take some part in their own treatment, you'll get some twats who will take any of this kinda talk as an insult to their authority or indication that you're some drug-seeking lowlife scum should just fuck off and die, basically. Haha sorry, jesus, excuse me, but this shit is unfuriating I know and I think it's a global problem to some extent.
There is generally a way to frame making the doctor or psychiatrist aware that you have done some research in a way that will alarm them less, if you just say you read some stuff on the internet that's quite vague and can raise suspicions (justly or not). If you read up more specifically on your countries prescribing guidelines, as I suggested above, and frame your enquiry this way ("I understand that usually you'll want to prescribe X or Y, first, but I'm unsure about that because Z, but I'm more interested in A, B, or C, because D..." - yknow? Hopefully that vague formula is clear) then you might have more success. It's possible that there are mandatory guidelines or laws as far as what they're even permitted to prescribe for a first line treatment, and it might be just SSRIs, so, they may not have intended to bluntly write off your hopes, but just are required to follow a certain set of steps...
One final point - SSRIs get a lot of hate here, but IMO some of that is unwarranted. Yes - they're mostly not that useful for a lot of people. But they are quite interesting substances IMO, not entirely ineffective for everyone, and they can be very effective for a very small subset of people with certain genetic variance in how the serotonin receptor responds to them, so try not to nocebo yourself about them based just on the (IMO, somewhat unfair) "big pharma bad"-oriented suspicion and unavoidably negatively weighted anecdotal stuff that you might see here, try to go through the steps they want you to go through - if you absolutely must - and keep an open mind that you might be positively surprised even if you don't end up prescribed what you were hoping for initially.
