I quit drinking recently (just hit a month wow), and so far it's been fine because I'm spending all of my time alone or working/doing errands. I don't like drinking alone so it's been fine, but where I live now the ENTIRE social scene is bars and clubs, so I can't meet anyone without being sober in a room full of extremely drunk people. I don't like clubs to begin with, and there's not really any quiet, sit down pubs around here where I could just get a soda and relax.
I used to pound drinks with my buds, but now that I'm seeing demonstrable health benefits of quitting (I have epilepsy and alcohol was giving me seizures) it's getting less justifiable to consider drinking again. I could smoke weed but it often makes me quiet and awkward when alcohol makes me outgoing and confident, which is what I really need right now. Also weed makes me shit at darts and pool.
Find some nice, relaxing non-alcoholic drinks. You can get virgin hot toddies, for example. Or a nice lavender-infused whatever. Like the other commenter said, you can also bring your own, at least as a backup.
Part of the relaxation is just having a nice beverage with fun people, having a little snack, and so on.
Also you might appreciate CBD so far as weed stuff goes. It's barely psychoactive (if at all), mostly just makes you feel a little fuzzy and relaxed. Also anti-inflammatory and helps with any pain. It might not make you feel like clamming up, could have the opposite effect since it tends to attenuate the effects of THC. It's nice to feel nice but not have a huge dopamine flash, just mild good body vibes.
Also to actually answer your question: I don't really feel uncomfortable around people who are drinking when I'm sober. The only time I might is when others get too drunk and are bothering people or making a situation dangerous, but that also makes me feel uncomfortable when I've been drinking, too. What makes you uncomfortable around the lushes? Is it just that you feel like the odd one out, or is it something else?
Also there has to be a place to sit down and relax somewhere. If it didn't violate opsec I could try to help you find a place, ha. Look for some alt music spaces with warm vibes, coffee shops that also have alcohol, food shops that are a little too comfy and laid back and are clearly meant to let people hang out for a few hours.