Hi there Mollybird22,
Thank you for posting to Apple Support Communities.
We understand that you can't change the sound of your alarm.
To begin with, have you tried restarting your iPhone since this issue started? A restart is a great first step in troubleshooting.
- "Press and hold either volume button and the side button until the power-off slider appears.
- Drag the slider, then wait 30 seconds for your device to turn off.
- To turn your device back on, press and hold the side button (on the right side of your iPhone) until you see the Apple logo."
Restart your iPhone - Apple Support
Then, test if the issue continues. If it does, let's make sure that iOS is up-to-date. These articles can be of help. When you back up, you can back up using a Mac or PC rather than iCloud if you choose.
How to back up your iPhone, iPad, and iPod touch
Update iOS on iPhone
After you've ensured iOS is updated, test changing the alarm again: How to set and change alarms on your iPhone - Apple Support
That should help. Let us know if you have any questions.
Take care.