Technologically, what you're looking for seems very straight forward. However, you'll need to determine the legality of offering a raffle. In the USA, it's considered a lottery/gambling and tightly regulated. From what I can see in a quick internet search, it's not legal for for-profit companies to have a raffle, but a not-for-profit may be able to hold an online raffle in some states. Here's a link: https://chance2win.org/us-state-online-raffle-legal-rules/
I'm guessing the legal issues are why you don't see any apps available. Can you tell us more about your business and what you're accomplishing with a raffle? There might be a sweepstakes option (also a regulated industry) that would be more viable.
Thanks for the additional info. I think your manual solution is the right thing to do while you're proving out the business model. Once you have some traction there, it might be worth it to hire a tech person to automate the drawing process. Good luck!
This is an unusual idea, such functions are usually used in browser games. In a game that I have been playing for a long time, this way the distribution of the lottery prizes won was realized. For example, on this site score88poker, you may notice a similar feature that you are asking about. If you want to somehow implement this in your business, you can borrow the idea from them as an example. I think you can find a lot of analogues, in order to take ideas for their implementation, you just need to know where to look for this information. I hope you find exactly what you are looking for.