Not sure if there are any apps specifically designed for banknote collecting.
I use Adobe InDesign to make a document for each series (Birds, Journey, Frontiers, etc.), and have one page for each note in my collection, and for each note I want to eventually have. Originally I started with one $2, one $5, one $10, and so on. Later I added one page for every possible signature combination. Later I added more pages for replacement notes, special serial numbers, etc.
I scan each banknote, front and back. As I obtain new banknotes, I add the scans to the appropriate page. Under each note, I list details such as catalogue numbers, where it was printed, the price I paid, and which prefixes/variants are the most valuable. The Charlton guide and our very own Serial Number Database have been the two most helpful resources.
Then the files are exported to .pdf for easy printing and portability. For those not familiar with InDesign, I'm sure Word or Pages would work just as well. I send the files to my phone and can easily scroll through the documents when at a coin store or a show, to quickly see which notes I have, which I'm missing, which ones aren't in good condition, and so on.
This is so much more helpful than a spreadsheet. For example, I had an otherwise Unc $2 with what looked like a tiny crease that I wanted to replace. A dealer saw my scan and told me that was likely just a counting fold, completely normal at the time, and not a deal-breaker.
While it took some time to create the first document (I started with Birds), after that it was easy to copy the template to other series. Plus, it's downright fun to research the details and work to improve the documents. Car enthusiasts can work on their cars and drive them, record collectors can listen to their records. For me, researching, scanning, cataloguing and searching for new notes is the equivalent of "playing" with my collection, but with almost no handling of the actual banknotes, and has provided countless hours of enjoyment. I'll upload a sample when I have a free minute.