Because you're having *that* problem, welcome to broadcasting too! You can't get the standard broadcast level without distorting, without some carefully tuned processing. If you slowly "just turn it up" with no processing, you'll clip/distort long before you get there.
The heart of that processing is a compressor. Its job is to quickly and constantly adjust the volume, to bring the softer parts up and the louder parts down. The more aggressive you set it to be, the more "processed" you're going to sound, so it takes some tweaking to get a sound that you like or are at least okay with. Some people use multiple compressors, with the later ones being progressively more aggressive.
Look up a bunch of YouTubes, articles, and other tutorials about how to use a compressor. They all work the same, with the same terminology, whether it's analog or digital or who makes them. So look at a bunch and see what "clicks" for you.
Compression can also bring out the background noise in what used to be acceptably quiet. So if you're only talking, and not playing music or sound effects through that channel, the first thing in the chain should be a noise suppressor. Then the compressor(s). And finally a "safety net" limiter as the very last thing. A limiter is simply a maximally-aggressive compressor, with slightly different controls because of the slight difference in how it's used.
So:
Raw Mic -> Noise Suppressor -> EQ? -> Compressor(s) -> Limiter -> Final Audio
The EQ and Compressor(s) can be swapped or interleaved, which makes a slight difference in how each compressor responds, but the very start and end of the chain should be the Noise Suppressor and Limiter.
A fair number of people use the Gain filter, but that's already included in the Compressor's makeup gain. Just use that, and keep the total number of filters to a minimum to do what you want.
When you get it all dialed in, the meter won't be all that useful anymore. It'll be near full most of the time, and may even tell you it's clipping, when it's really not. If you really want to make sure it's all correct, you'll need to disable the later filters and progressively enable them down the line, and see what the meter does at each point.
The raw mic should have a decently strong signal with lots of headroom (adjust the physical preamp if not; don't use OBS's gain for this), and then it should be progressively more predictable as it goes through the compressor(s), but not all the way up yet because it's not *completely* predictable yet. Only the final limiter should have it all the way up, and you know it's not actually clipping because of its settings, not because of the meter.
