Sorry you’re having trouble with the featured image. Some details that will help the community solve the question: What theme are you using?
Without knowing what theme you’re using, one approach you might try is removing the featured image from the post/page, then click update. If the featured image is removed, you might then be able to choose another featured image.
Another option would be to stop using the Media pop up window and updated the featured image from the Featured Image meta box on the Edit Post screen.
Edit to add the solution from the comments
If you tried the above and it didn’t work, the next thing to do is switch themes, then attempt to change the featured image. If that works, then the issue is with the theme, and you might need a new copy of the theme. If that doesn’t work, try deactivating all your plugins and then attempting to change it. There may be a plugin conflict as well.