No, but there are some things that ostensibly take place in public but should still be considered private, absent some urgently pressing higher need that can only be met by disclosure.

To the extent that a given condition is public people are allowed to note that. This is why assholes were legally allowed to call me pimple-face, for instance.

At some point of excess, wouldn't that fall under verbal abuse, harassment, or bullying, depending on whether you're considering laws or school policies, and thus not be considered free speech?

In general I believe people should be able to say anything they want, but if what they say or to whom they say it violates someone else's rights, their victims shouldn't have to put up with it.