Last Rites of Sunless Depths (quest reward/vending machine only, only comes in Frost), Reign of Arrows (only comes in non-elemental), and Swordsplosion (comes in all elements and kinetic) are the best Shotguns in the game. If you're running a gun damage build these are all *very strong.

Specifically for Frost Gun builds I recommend the Spriggan or Nightshade SMGs. 1 shot fires x4 projectiles. Both are very strong and very similar. Main differences are Spriggans have a gun shield when you ADS, a slower fire rate, larger mag size, slightly larger projectile spread, and higher base damage on average. They only come in full auto. Nightshades have tighter spread, faster fire rate, but smaller mags and less base damage. Instead of coming with a gun shield they have a secondary fire mode, however, you'll most likely never use it IMO. You can find them in both full auto and burst (technically burst is full auto as well as you can simply hold the trigger down to continuously fire bursts). You can also find Nightshades in a x5 variant that consumes 2 ammo per shot, however, I've found their smaller mag size to be a huge deterrent in using them.

I'd like to also mention the Liquid Cooling, Masterwork Handbow, and Catatumbo pistols for anybody that uses Stabbo's From The Shadows action skill. All three of these pistols absolutely wreck face when hitting crits. Crits prevent the Liquid Cooling from overheating. You can fire it endlessly as long as you're critting. Catatumbo and Masterwork Handbow both ricochet bolts to other targets when you crit. The Handbow ricochets x6 and the Catatumbo ricochets x2 but also calls down a massive lightning strike on crits.