Hi, welcome to iPF!
If you search for apps that can edit photos in App Store, you'll get quite a few results. Some of them can store the pictures as well.
Here's a small collection of apps that I know or use:
Snapseed - editing photos
Photoshop Express - for editing
Photogene - editing also
Adobe Lightroom - editing and storing, there's also computer software
Flickr - storing (1TB) and editing; there's also a "private" setting, if you don't want to show your pictures to the community
There's also Apple's iPhoto app.
I don't know, though, if they are capable of stacking photos. You'll have to take a look at them.
There are also True HDR and Pro HDR. I suppose they are not what you're looking for, but you can try.
There's also Easy Photo Stack - paid and free version. Supposedly this is the kind of app that you're looking for.
Hope that helps.