You can animate with Photoshop. It's not the easiest software to do it in, but you already have it and some artists are able to create some amazing things with it. Here's a list of animation software I have used. All great in their own way.
ToonBoom Animate (expensive, but probably the best)
ToonBoom Studio (lighter version of the above)
Flash (my Favorite)
After Effects (great puppet tools and for special effects)
Maya (3d)
3ds Max (3d)
FlipBook (mainly hand drawn animation)
Anime Studio (popular & affordable)
TVPaint (expensive)
Animation HD (iOS app)
AnimationDesk (iOS,Mac,Android)
Free:
Synfig Studio (Mac, Windows, Linux)
Pencil (Mac, Windows, Linux)