How to build a good ‘stagger lock’ character

In Dark Souls 2 you can consider infusions and the +N upgrades as two separate properties of the weapon. For example, if you have a +10 Claymore and infuse it with lightning, you'll have a +10 Lightning Claymore. Further, you can "uninfuse" it and it'll go back to just a +10 Claymore. There's no upgrading of the infusions themselves. That said, if you infuse a less than +10 weapon, you can still continue upgrading it to +10 with titanite, and it will retain its infusion as you upgrade it.

Whether or not to infuse a weapon is another question. Each infusion does something different to the weapon. Something like Lightning will take away some of the base damage on the weapon and replace it with lightning damage. This also affects the scaling. A purely strength based character probably wouldn't want to infuse with lightning, since doing so would likely lower the scaling off of strength and add scaling for lightning (which is affected by Faith). A Strength/Faith hybrid build might do a lightning infusion, though.

There's so many combinations, and each type of infusion works differently (Raw increases base damage but lowers scaling, Mundane adds scaling based on your lowest stat, etc). My best advice would be to experiment with different types, as there's not necessarily a "right" answer (keep in mind that you can preview the changes before you actually go ahead with the infusion). It depends a ton on your build and playstyle.

The only thing that would be similar to it would be the Ring of Thorns or the Pyromancy Immolation, but both do not work as you described.

When the Ring of Thorns procs (it doesn't work on every hit, only on a %, based on the ring level) it shoots out some darts (see this video at 0:58).

Immolation sets the caster on fire, so you would have seen it.

What probably happened - you encountered a cheater (likely) or lag