Hey there, xinyi244!
Thanks for using Apple Support Communities! From your post, it sounds like you set up Screen Time on your iPhone, but are not able to access an app after reaching limits. We'll do out best to help with this!
You've taken great steps so far! To confirm, did you disable App Limits completely, or only for the YouTube application? If you only disabled it for YouTube, try disabling App Limits from Settings > Screen Time > App Limits.
Should the behavior persist, try turning off Screen Time, then access your app again. You can do this from Settings > Screen Time, scroll to the bottom then tap Turn Off Screen Time. Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support
If the issue continues and you're unable to access the app, Contact Apple Support.
All the best.