Interesting problem! :)
Anything with a checkmark has an associated meaning with "done" or "completed". That's probably also why the majority of getting-things-done apps use this symbol as their icon; and simply the name of "checklists" indicates you finished checking stuff.
It will be even more distinct if you remove the square and only use the checkmark in a corner of the photo. This reduces the visual cues for something being "selected" and focuses more on just being "done".
It is better to come with an alternative for the "selected" state, for which the checkmark is a lesser choice, especially in combination with needing a "processed" state, as you noted.
Small changes would already increase the distinction with a completion state by using a cross [x] instead of a checkmark (including the square around the cross), or a filled square, colored dot, etc.
Making a visual cue for selection is likely to be easier than for completion because you can give immediate feedback to the user, and the selection is easily undone (e.g. it's easier to explore & find out the meaning of this visual cue). For completion, it needs to be clear instantly because you don't just "try out" this kind of interaction and then undo it.