Need photos but iPhone 6 is in recovery mode

If you had iCloud Photo Library turned on you can log in to https://www.icloud.com/ and look to see if they are in the Photos app there.

If they are not, another possibility is that the phone was set to back up to iCloud. If so it would automatically backup while charging if connected to wi-fi. The contents of the backup won't be visible at icloud.com but can be used to restore to an existing or replacement iPhone: iCloud: Restore or set up your iOS device from iCloud

As an active ASC member I have read many cases just like yours, sad indeed. I hope you are able to retrieve your photos somehow.

I know that this will not help your current situation but in the future I suggest importing your photos to a computer on a regular basis and backing up the HD on the computer as well. Upgrades generally go well as you said but when they don't, data on the phone is usually lost, sad to say.

Import photos and videos from your iPhone, iPad, or iPod touch to your computer - Apple Support

Once the phone is in Recovery Mode it has been erased. You will not be able to recover what was on it unless you have a recent backup stored on your computer. Then you can restore the backup after recovery.

iPhones do not have a hard drive. Storage is solid state. Upgrading and restoring requires erasing the memory. Once this happens everything stored in that memory is erased. If you have seen third-party software claiming to recover such data, then you can give it a try. Be sure not to use any that requires jailbreaking first.

Sub-Two wrote:

Is there any way to confirm the idea that photos and video that don't appear on iCloud.com are actually there so that if I fully restore the phone to factory like it's telling me, when i connect it back to iCloud that it would push the non-showing files to my phone?

You can confirm the existence, the size, and the date of an iCloud backup but there isn't a way to see the contents without doing a restore to an iOS device.

I understand, and that is why there is backup. Backups can be in the cloud, in iTunes, in Photos, etc. If you don't backup and something like this happens, then you can lose your precious data. Again, iDevices no longer have "drives." It's all just flash memory - Erasable EPROMs. Once they are erased they are empty until reprogrammed.

Have you looked in iCloud.com? They could possibly be there depending on how you had your phone configured.