22 Long Rifle ammo is finicky. Tell us all about it here.
The guide in the picture does look like one made for an annie but I can't tell for sure. I think I use a brush about 1 or 2 times a year. I use a jag and a patch when I clean the rifle. Most of the lead build-up is within the first 4 or 5 inches of the of the chamber. Sometimes you can get a big build up called a doughnut right where the rifling starts. It is a little tougher to get out. Some JBs bore cleaner on a patch seems to work the best foe me to get rid of that problem.