For recovery mode on the iPhone 7, it's the Power button (right side) and Volume down (left side), keep hold both at the same time, until the iTunes logo comes up. With it going to SOS mode kind of sounds like defaults were changed (probably Accessibility). If you still can't get it to to go and you use iCloud and Find my iPhone. Go to the website, https://icloud.com/find and sign-in with your Apple ID and click on your phone, as long as it doesn't say Offline, click it and hit Erase then hit remove from account. This should be instant as long as your iPhone has a working signal (Wifi or Cellular)
This process has the same steps as putting it into recovery mode and using iTunes with the exception it doesn't reinstall iOS from the ground up, just erases your data and settings completely.
If that still doesn't work, turn your phone off completely with just the power button, and then after it's off, hold down just the Volume down button, as you plug it into your computer with iTunes open, let go of Volume down when you see the iTunes logo on your phone screen. If neither of those 3 options work, you may want to take it on in for service. Usually to trigger SOS on the iPhone 7, you have to hit the power button 5 times back to back.
