Through co-design interviews ($N=19$) and a design evaluation survey (N=136) with U.S. teens ages 13-18, we investigated teens' privacy management on social media. Our study revealed that 28% of teens with public accounts and 15% with private accounts experience "dysfunctional fear," that is, fear that diminishes their quality of life or paralyzes them from taking necessary precautions. These fears fall into three categories: fear of uncontrolled audience reach, fear of online hostility, and fear of personal privacy missteps. While current approaches often emphasize individual vigilance and restrictive measures, our findings show this can paradoxically lead teens to either withdraw from beneficial social interactions or resign themselves to accept privacy violations, viewing them as inevitable. Drawing on teen input, we developed and evaluated ten design prototypes that emphasize empowerment over fear, system-wide explicit emphasis on privacy, clear privacy norms, and flexible controls. Survey results indicate teens perceive these approaches as effectively reducing privacy concerns while preserving social benefits. Our findings suggest that platforms will be more likely to protect teens' privacy and less likely to manufacture unnecessary fear if they include designs that minimize the impact on other users, have low trade-offs with existing features, require minimal user effort, and function independently of community behavior. Such designs include: 1) alerting users about potentially unintentional personal information disclosure and 2) following up on user reports.