Welcome to the Support Communities!
The article below may be able to help you with this issue.
Click on the link to see more details and screenshots.
As a first step, I would suggest restarting / resetting your iPhone:
If that does not resolve the issue, refer to page 146 in the iPhone User Guide to Reset All Settings:
iPhone User Guide for iOS 7
Here are some additional steps to troubleshoot Photo Stream:
I found a solution that worked for me https://discussions.apple.com/message/23387322#23387322
Randers 4 said: If you haven't already done so, you might want to go to control panel>uninstall, right-click on iCloud on the programs list and select Repair. Then restart your PC and try photo stream again. If that doesn't resolve it, try uninstalling iCloud and reinstall the latest version from here: http://support.apple.com/kb/DL1455.