If you just want to visit Nanwan Dam, I suggest that you wait until after 6: 00 p.m., when the managers are almost off work, you can ride a motorcycle or something, or just walk in and pretend to be a local person (we Xinyang people go swimming directly at night). Don't take a taxi, it's easy to be stopped.

As for Swallowtail Island, if you just want to play with water and eat something, find a taxi and let him take you there. I have forgotten the specific way. Anyway, let him take you to Swallowtail Island and tell him to go to a place where you don't need tickets. . . It may not be very detailed, but in short, find someone you know in Xinyang, and I believe I can give you a better answer.