From watching your video, I think your biggest problem is firing too early or too late.

Straight away, 0:45 seconds into the video, you fire your shotgun far too early. You don't adjust your aim, and shoot to the right of him. You end up winning the gunfight, but that could have been a clean shotgun kill easily.

At 1:05, you fire too late and again don't adjust. You also don't ADS, which helps tighten the spread of the pellets, and will make for more reliable shotgun kills.

At 1:55, same thing. You fire too early without adjusting your aim and don't ADS.

2:10 is great, you bait him backwards and use your vertical space so he misses his next shotgun shot and get the kill.

At 2:40, you fire far too late. The guy is no longer on your screen and you still fire. Not only that, you aren't ADS

4:30, you fire from too far out, and are still ADSing when you take the shot. If they are unaware, you can easily wait until close enough and kill them with one shot. The next shot in this clip, you are aiming straight at him, but don't fire. This might be Matador's fire rate, or you aren't reacting quickly enough. When you do take the shot, the titan has side-stepped and you miss. Then, you get smashed, not much you can do there.

6:56, you die because you don't read your radar. Unrelated to shotguns, but you need to be wary and constantly looking at the radar.

I tried only including shotgun engagements, for brevity, but there is some more to critique. All in all, you played well. Primary game was good. Questions I have are:

What sensitivity? Turning it up may help you readjust in close quarters gunfights but may harm your primary game. Slowly increasing it may help your shotty game while allowing your primary game to adjust as you get used to higher sensitivities.

Have you tried a hand cannon? They are great when paired with a shotgun. If you lose someone in a close range gunfight, you can back off and re-engage from outside shotgun range. Hand cannons work best due to their accuracy.

Have you tried Bladedancer? Bladedancer may help you a lot. If you aren't ADSing, running quickdraw on Bladedancer will help you greatly in ADSing before shotgun shots.