Good brawler.. well you're definitely not a pure boxer and throw heavy punches instead of hard punches. Generally short well built people choose that style, pressure fighter and usually a '4 round' fighter. Accuracy wouldn't be too great but still able to shake opponents even if they have their hands up. Can easily be countered so a strong chin & neck is required also.
I'd suggest trying to apply intelligent pressure, before trying to brawl with someone. Brawler implies, at least in my mind.. sloopy punch technique (leaves huge openings when throwing due to loading up on shots). Someone who is worried much more about inflicting punishment on you, then avoiding it (meaning lack of head movement..) I would never suggest to someone to try to "become" a brawler.. Swarmer or Pressure Fighter.. who both can have very similar characteristics of a brawler, but without the getting punched in the face.