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.

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

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

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