The Brotherhood has always maintained an interest in pre-war weaponry and technology oriented around violence. So long as you stick to some of the more potent explosives (C4, fat man, plasma/pulse grenades, etc.), I think you could justify using explosives.
BTW, while the Brotherhood is known for its extensive use of energy weapons, it still has several notable paladins that have used explosives. Furthermore, it is a BOS paladin's body that is found beside the unique grenade-machingun "Mercy." You could perhaps say that due to your character's rebellious nature (perhaps the very reason you left the BOS), you use the much more destructive and less-common explosive weaponry than the hackneyed energy weapons with which the BOS has become so closely associated.