Do I need a virus protection for my Mac Catalina?

I was told I was infected by some weird message.

Effective defenses against malware and other threats - Apple Community describes that scam:

• If you encounter a website, text message, email, or phone call alleging your Mac is infested with some ick or that you need to take immediate action lest dire circumstances ensue, it is 100% fraudulent. Ignore it. Read Avoid phishing emails, fake 'virus' alerts, phony support calls, and other scams.

Responding to that scam is what gets people into trouble. Phony "tech support" / "ransomware" popups and web pages - Apple Community has a few illustrations of them. Installing some "anti-virus" thing is an inappropriate response that is likely to cause real problems, as opposed to the phony problems those scams allege.

Don't believe everything you are told. There is a great deal of misinformation out there.

Also, see: Recognize and avoid phishing messages, phony support calls, and other scams - Apple Support

No. Being knocked offline has nothing to do with viruses/malware.

See: Effective defenses against malware and ot… - Apple Community