Welcome to Android Central! It's highly unlikely that you got malware from watching a video on YouTube (assuming you were using the YouTube app, and not on some random website with an embedded YouTube video on it).
What anti-malware app did you try to install? Are you saying that once you installed this app, the anti-malware app immediately warned you of malware on the phone?
Which Alcatel phone do you have? Try wiping the cache partition to see if that helps with any glitchy behavior.
https://support.t-mobile.com/docs/DOC-33038