I want my app X to be able to create issues on the private repo Y for app X.
Basically in app X I want to create an input form similar to that of the new issue form on GitHub. Where there's a title, comment, and just labels.
Is there an API out there that will allow me to do this?
Use official github api for creating issues via any app. Here is a link to the github issues api. Below is an example.
POST /repos/:owner/:repo/issues
You have to include parameters required for creating issues like title, body, assignees etc.
Also you have check github oauth flow for github api since you are creating issues in private repository