Common truisms I've heard (especially in Feb-March, but still occasionally these days) is that "worry and panic is worse than the disease itself" or that "the most important messaging during a pandemic is "don't panic.""
It's relatively easy for me to find examples of significant potential harms of excess panic (eg, anxiety, agoraphobia and other psychological issues, fear of going to a hospital for other emergencies, racially motivated or otherwise outgroup violence).
But when I look at historical examples of actions during pandemics, it was hard to find *any* examples of lots of additional people dying or a pandemic otherwise made much worse by excess panic, while it was comparatively common to find examples of pandemics made much worse by insufficient worry (NunoSempere has a list here).
If there are historians or history buffs among this group, I'd love to see people provide counterexamples illustrating when excess panic makes pandemics much worse.
It's a bit different than what you are looking for, and historical cases are earlier than would be relevant directly, but there were certainly many documented cases of pogroms happening during various epidemics during the middle ages and Renaissance when a minority group (usually Jews) were blamed and massacred.
This isn't quite what has happened so far, but I can certainly imagine a case where a modern pandemic could similarly exacerbate class or racial tensions leading to violence.
No worries! :)