Argh, we know how frustrating this can be! This is a known bug with smart phones, such as the iPhone, when photos are taken vertically (phone in the upright position) but bonus...it can also randomly affect other photos too! While they may look correct on your phone or desktop, they may upload to Adopt a Pet (and other websites) sideways.
Fun Fact: Photos taken horizontally usually will not have this issue!
Pro Tip: If you've already taken the photos, you may use a free online photo rotating tool, which will let you re-save the photos with the correct orientation, then you may re-add them to your pet's listing.
If you have a photo editing application on your computer already, you may try opening the photos on your computer, making sure they are not sideways, then using "save as" to save each photo as a different file with a different name. Often this will save them without the orientation bug embedded in them.