Apple care plus is not visible in check coverage

That does not indicate a problem with your AppleCare, just an issue with the Apple servers. In checking now, all services are green, Apple - Support - System Status however, if you continue to have issues, then use the Get Support link at the top of the page here and you can contact Apple Support to answer your question. However, if you go on your iPhone to Settings>General>About, you can scroll down to AppleCare+ and it should display your expiration date, and if you tap on it, it will take you to a page displaying your coverage.

What is appearing when you check your serial number? Do you have a receipt for your AppleCare+? You should also have an email with your coverage information.