Hello Bronto33,
Apple Support Communities is a great place for help! App limits is a wonderful feature, and ensuring that you're seeing accurate information is important. Although you don't have the YouTube app installed do you visit the YouTube website in Safari or in a different web browser?
If so, and that website is still open, or are you receiving messages that contain links to a YouTube show? Also, have if you don't want the app installed, and are confident that it's not installed have you checked your App library, or verified if the app is installed by searching for YouTube on the device, or in the App Store?
Use Screen Time on your iPhone, iPad, or iPod touch
Have a great day!