Hydroxychloroquine is being promoted as a treatment or prevention for COVID-19 based on questionable evidence. The long-term impact of hydroxychloroquine on the retina introduces another reason to be cautious about its use outside of clinical trials.
Can vigorous adjustment of the neck cause direct injury to your eye? Probably, but I don't know. This is based on a single case report. Still, I wouldn't take the chance. And why do I keep mentioning dugongs?