This is all a bit over-simplified, so please forgive me if you know already...
'volume' in digital terms has an absolute maximum, unlike analog which you can 'push a bit' without it getting unpleasant.
As Jim Mack says, checking for 'clipping' [squared off waveform tops] is an indication you have passed this limit.
If, when you analyse the file visually, only a small number of peaks are reaching full volume, the standard method of increasing the overall apparent loudness of a sound is to compress it, or even brick-wall limit. [many varieties of both compressors & limiters are available as plugins for all DAWs, including some 'mastering' plugins that allow compression by frequency]
This will bring up the overall sound level, whilst holding back the peaks to prevent clipping. You can be as subtle or as fierce as you like - but the noise-floor will rise [though that's not what I think your essential problem actually is] & the more compression you add the more 'squashed' the result will sound; but many pop records are mastered this way to make them appear 'loud' on the radio [so much so over the past 15 years that if you don't you'll sound quiet compared to the rest]
Post a comment if you need more info or clarification.