It can depend on the GP but might be worth asking specifically for anxiety meds or something for trouble sleeping. I know if feels awkward af but you can say 'no' to what the doctor suggests.How did you get them? I’ve only been to the GP about this once, just got offered some sort of therapy and anti depressants which I didn’t want as that’s not the issue!
I had the opposite problem when I first went on medication - I mentioned depression and anxiety and my GP only focused on the anxiety. Prescribed me literally 3 months worth of of propranolol, a kind of beta blocker which didn't really help because I didn't really suffer panic attacks (and had told her this), and told me to come back in 2 weeks. The first thing she said when I said when I came back 2 weeks later? "Well, we didn't think they'd work, did we?" Like, why prescribe them then? I really struggled in between those two visits (esp having such a large quantity of meds available) and I wish I'd been able to just say 'no' as much of a nightmare anxiety makes that word.
I hope you're doing alright though I know anti-depressants aren't for everyone but they can help with anxiety too (my current ones definitely have) although there can be a lot of trial and error involved