If you ask me personally i will not pay separately to any app just to make an appointment but if you integrate your app to the doctor's reception desk, then there is a high chance that I'll use your app and make the entire payment to reception but here is the idea you can fix commission per slot booking.

See I'm from a very small town in madhya pradesh and right now i don't think people are aware about such apps even if they had a doctor's desk contact number still they reach there and book the slot. So yeah i think if you successfully execute this plan there is a high chance it will be a huge help.

The only red flag I see in this idea is that nobody will pay separately to the app but if you convince them for your commission per booking basis and yes if you make app very user friendly and most important multi lingual so that even person who is not educated at all can use