Yes. But you might not want to.
The general rule of thumb is: anyone can sue anyone else, at any time for any thing. However, I believe in this case you would need to show actual damages. I don't think emotional distress qualifies as actual damages. That type of thing is usually awarded as an add-on to something like a personal injury case; it's usually called "pain and suffering" if I'm not mistaken. Emotional distress is usually not compensated.
To your question about suing an app: you can always sue, provided you can find an attorney to represent you; but you are likely to encounter a few challenges.
Firstly, suing apps is a new area of law. So not much case law exists. This will present a challenge to your attorneys as well as to the courts.
Secondly, it could be difficult to find the owner of the app. It depends who owns the app and how much care they have taken to conceal their identity.
Thirdly, establishing jurisdiction can be challenging. Apps can run from servers anywhere in the world. App developers are extremely mobile. Suing a rogue developer operating inside an unfriendly country, for example, could be prohibitively expensive.
Fourthly, under the most favorable scenario considering the above questions, it's unclear what damages you've suffered and how much liability the app owners bear in proportion to, say, the app user i.e., your soon-to-be ex-husband.
Lastly, if you win and the app owner lives in a different country, has few assets or his assets are "judgment resistant," collecting your damage award could have its own set of challenges, obstacles, hurdles and roadblocks.
All things considered, it could be an uphill battle all the way and at a minimum very expensive. If not prohibitively so. I'd say it's a long shot.