Sometimes it’s an iterative process… You compress and then go-back and EQ.
You might try limiting instead of compression. It’s easier to set-up and there are usually fewer side-effects.
If you don’t know this, limiting is a kind of fast-compression that pushes-down the peaks. Then you can use make-up gain or normalize to bring-up the overall volume.
But the limiter doesn’t have the noise-floor adjustment so it’s going to boost the noise along with everything else.