Going out solo works totally fine. If I'm out at night doing game more often than not I'm solo. It makes no real difference to your game or the standard of your night at all after a while, I'd take it any day over heading out with some LSS mouthbreather wingman I barely know. It's good for practise too, because it forces you to actually do stuff instead of just standing about.

You can't expect fun to come to you just because you wandered into a club. The right mood comes from the right set of actions. You do stuff to get in a good mood, you don't wait for a good mood to hit you before you do stuff.

Going out solo works totally fine if you do it right, but you can't stand around waiting for an opportune moment to talk to someone or for something to happen. You've got to start chatting to people straight away, the minute you get in there, or even before on the way in or waiting in the queue. Otherwise you'll end up standing about and feeling awkward and it'll just make it harder to get out of that headspace.

If a nightclub feels too intense at first hit up the smoking area or go to a smaller bar where it's less loud, then you can hit somewhere else once you feel more social and comfortable. Don't feel awkward about it, it's totally normal. Remember people who are out want to talk to new people. That's pretty much the implicit point of going out in the first place.