Hello lindsjohnson24,
It may help to reset your iPhone by holding the Sleep/Wake and Home button at the same time until you see the Apple logo on your iPhone's screen.
Turn your iOS device off and on (restart) and reset
http://support.apple.com/en-us/HT1430
If you're still unable to set an alarm manually, the next step would be to place your iPhone in recovery mode (shut down the device and hold the Home button while connecting it to your computer) and choosing "Update" when prompted. This will reinstall iOS 8, but will leave your information in place.
- Make sure that you have iTunes 12 or later on your computer.
- Put your device in recovery mode.
- When you get the option to restore or update, select Update. This will reinstall iOS without erasing your data.
If your iPhone, iPad, or iPod touch doesn't respond or doesn't turn on
https://support.apple.com/en-us/HT201412
Sincerely,
Allen