How do you fight brawlers/swarmers?

I'm not sure if brawler is the right term or if its slugger or swarmer or whatever. anyways, i was sparring with this dude and he just kept shooting his right hand on every punch. my reaction to this was to duck underneath it, but i couldnt get my punch of because as soon as i ducked, we were in a clinch. anyways, im a boxer, i dont really like fighting guys who put a ton of pressure and just start throwing power punches but at some point im going to have to. so i was fighting a short dude, lots of power, and just kept coming at me with right hands. sometimes he didnt even hit me , but i felt like i couldnt see. how should i fight these type of dudes. my thinking is next time i spar with him, move my head and then jab, and then just use a lot of lateral movement. what do you guys think?