With the emergence of the COVID-19 pandemic, the political and the medical aspects of disinformation merged as the problem got elevated to a whole new level to become the first global infodemic. Fighting this infodemic is currently ranked very high on the list of priorities of the World Health Organization, with dangers ranging from promoting fake cures, rumors, and conspiracy theories to spreading xenophobia and panic. With this in mind, we studied how COVID-19 is discussed in Bulgarian social media in terms of factuality, harmfulness, propaganda, and framing. We found that most Bulgarian tweets contain verifiable factual claims, are factually true, are of potential public interest, are not harmful, and are too trivial to fact-check; moreover, zooming into harmful tweets, we found that they spread not only rumors but also panic. We further analyzed articles shared in Bulgarian partisan pro/con-COVID-19 Facebook groups and found that propaganda is more prevalent in skeptical articles, which use doubt, flag waving, and slogans to convey their message; in contrast, concerned ones appeal to emotions, fear, and authority; moreover, skeptical articles frame the issue as one of quality of life, policy, legality, economy, and politics, while concerned articles focus on health & safety.