Nah, you're just making things up and haven't provided any valid evidence to justify restrictions on free speech. Stupid people have always believed stupid things since long before social media. Remember the days of forwarded hoax email chains?
Words are not harmful, unless they're a specific and credible threat or incitement to violence. People claiming otherwise are defining down "harm" to such an extent as to make the term meaningless.
Once people start saying speech is violence I exit the conversation. Generally said by the most white bread privileged people because they've never experienced actual, real violence.
The ironic thing here is that the main reason you've seen that kind of claim is because social media tends to spread the most outrageous / novel / radical kinds of speech (in turn further causing radicalization among the recipients of it)
More discussion about vulnerability to cognitive biases, speech that abuses and exploits them. https://www.youtube.com/watch?v=jzzjbSkrLCQ and how social media design supports and reinforces this kind of speech over others.
To see what I mean by harm, read the threadreader link.
My best idea so far is similar to the solution we had for yellow press and tabloids. We learned to recognize and be aware of manipulative kinds of journalism. If we are all careful, more aware and more skeptical - especially on social media - there will be less opportunity to be duped.
But this is a very old game of indirectly signaling one's pretensions of superior human quality by implying that things others consider harmful are do not qualify as harms to themselves, and thus less important than the freedoms that they desire to have, some of which may inflict those harms on others.
Words are not harmful, unless they're a specific and credible threat or incitement to violence. People claiming otherwise are defining down "harm" to such an extent as to make the term meaningless.