Again, I have an iPhone 5 running iOS 8.2 and I still see the ability to go to any of my photo Albums for the Facebook app.
So, your issue is specific to your device. Back up your device to iCloud and then Reset All Content and Settings to Factory reset your device. Sign onto it without restoring from your backup, but sign onto iCloud so that your Photo Stream downloads. Take a couple of photos, and then download the Facebook app to see if you can now see the dropdown.
If you can, then Reset All Content and Settings again and restore the device from the backup you did earlier. Once everything is back on your device, go to the Facebook app and see if you can see the dropdown. If you could see if from the "clean" install, and you cannot see it now, then it is either an issue with the settings or an issue with the content on your device.
Cheers,
GB