Irritated with the nomination process.

Hello everyone, I have had two nominations rejected recently as duplicates, however there are no poke stops in either location. One is our public library, and the other is a 100 year old auditorium built by one of the town’s founding families.
there is no option to appeal, so how do I move forward?
Comments
You only get one appeal every 30 days. Having said that, you have to keep in mind that each Niantic game has its own rules regarding spacing of wayspots, which means that not every accepted wayspot will appear in every game. It is very likely that both of the locations you nominated already exist in Niantic's database and were correctly marked as duplicates but are too close to other wayspots to appear in Pokémon GO. You can verify this by returning to the locations in question, pressing the New Pokéstop button, and looking for the reddish pins on the map, which represent existing wayspots that are not eligible to show up in Pokémon GO. (This is a relatively new feature and may not have been in-game when you made your nominations.)
Assuming they are already in the database (and already in a correct location), there is nothing to be done as the process is working as intended.
they do have pins for the library, however they are in the wrong spot, and the stop was never added into the game. There are poke stops near by, but no closer than others that already exist in the town, and further away from other stops I have seen playing in nearby city’s .
Pokémon Go uses a grid system to limit wayspot density (level 17 S2 cells). Only one Pokéstop or Gym is allowed per cell. Any other wayspots in an already occupied cell will not be eligible to show up in Pokémon Go.
Because these cells are quadrilaterals, this can result in two Pokéstops being right next to each other if the cell border runs directly between them, but can also result in a wayspot that's sometimes 50 or 60 metres away being considered "too close" to go live in Pokémon Go. So that's why you may see Pokéstops much closer together than what you tried to nominate, but why the library does not show up in game (and probably the same applies to the auditorium as well).
If the in game location for the library truly is inaccurate and needs moving, you can request it by going onto the help page on Wayfarer and tapping the orange speech bubble icon in the corner to bring up the support chat. Just be aware though that if it is already accurate and you try to move it anyway, that could be considered abuse.
When you nominated your Pokestops, did you not look at the map in PoGo and notice that there were existing Waypoints very close to the ones you were nominating, perhaps even with the same or very similar name (Library?).