There's probably an app that will do that, somewhere; but I don't have one.
I could jury rig something, sort of.
FormConnect lets you make you own form based database. It won't warn of duplicates, but it will let you search for records. So, you could first search for a record, then add it if it doesn't already exist.
You could do the same thing with the Contacts app, if you don't mind cluttering your contacts with lots of non-contact information.
I'm pretty sure you could make a Workflow that would do this, storing either a text or jason file on Dropbox (or somewhere else). How flexible and powerful it would be would be up to the skill of the person building the script.
That's all I've got, other than continuing to search the App Store for something designed to do exactly what you want. Try searching for list apps, and maybe 'unique list' apps.