Photos that are taken are being rotated in different ways

Yep that is what I was asking. There have been reports of using the Camera in Instagram or using a third party camera app, where this has occurred and later resolved by updates that the respective developers provided. I have not see this reported using the Camera app installed with iOS, so just making sure we are talking about the same app.

When taking the picture, there is a little green dot that appears in the corner of your screen that tells you the camera is in use. Do you see this dot in the upper right of your screen, or the lower right corner of your screen?

There are also 2 things you can do that may resolve a glitch using the Camera app:

• Force close the Camera app - Close an app on your iPhone or iPod touch - Apple Support
• Force Restart the phone - This may take a couple of attempts to get the speed and sequence of the key presses correct and the last step of holding the side button until the Apple logo appears could take up to 20 seconds. Ignore anything else you see on the screen during that time.

Force restart iPhone - Apple Support

Is this when using the default Apple Camera app, or when using another app that allows you to take pictures?

Good news! The dot location was just to check if your gyroscope was working correctly with it appearing in the upper right as it should be. All is well.