So I emailed Samsung customer support and basically they told me to clear my cache and reset app preferences. I'll post the instructions they sent me below. We'll see what happens.
Thank you for taking the time to contact us at Samsung Technical Support. We always appreciate hearing from our customers.
After reviewing your e-mail, I see that you are experiencing issues with the S7 Edge phone's camera as it will not save the picture. I will assist you with required information.
Let's try a few troubleshooting steps to isolate the issue;
1. Reset app preference:
a. Please go to settings.
b. Tap on applications, select application manager.
c. Now tap on more and select reset app preference.
NOTE: By performing the reset app preference the settings of applications will be reset on your phone.
2. Reset Camera settings:
a. From Home Screen>>tap on Apps.
b. Open Camera application>>tap on settings.
c. Now tap on Reset settings.
3. Clear Cache and Clear Data for Camera application:
a. Please go to settings.
b. Tap on applications, select application manager.
c. Now select Camera and tap on Clear Cache and Clear data.
d. Tap on OK
Please check if issue persist, if issue persist, please get back to us so that we can assist you with further information.
I hope the above information is helpful.