The multiplayer in the game sucks. Now I remember makin comments like this for Halo 1 with the pistol and for halo 2 with the BR. In destiny, it's the shotgun. The multiplayer is heavily weighted in favor for the shotgun. To the point that it is a severe disadvantage for anyone who uses anything but it. It's very sad, especially with all the unique abilities, to have a game that is so predominate with close range combat.
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Change your strategy. Arm a good AR. Start taking different routes. Back out of small rooms where there's chaos. Back up. Draw them out of the room and then fill them with bullets from a distance. They're not going to stop using shotguns so you have to change your approach to PVP. Simple as that.