I'm almost 100% sure the 22 brifter is the same part. 1 vs 22 seems to simply referred to 1x11 (1) or 2x11 (22). Confusing naming but on the 22 spec you would have one brifter with 2 gears and another with 11. On your bike you just have one brake and one brifter, the 11 speed.
So you just need a new SRAM Rival 11-speed brifter, which should be the same on both.
As for changing them over, you may as well replace the cables while you're doing the change. You'll need to remember to shift all the way down so that the holes for the cable line up nicely. Tons of YouTube videos on how to do this.
You will likely also need some cable cutters, a 5mm hex wrench and whatever tools the brifter needs for opening/loosening.
You will need to adjust the gear cable tension to ensure smooth shifting. This should only require tightening or loosening using the barrel adjuster on the derailleur, and shouldn't require any changes to the high or low limit screws on the derailleur. Again, plenty of YouTube videos for this.
Good luck and if in doubt, go to the bike shop