Data voids--areas of the internet where reliable information is scarce or absent--pose significant challenges to online health information seeking, particularly for users operating in low-web data languages. These voids are increasingly encountered not on traditional search engines alone, but on social media platforms, which have gradually morphed into informal search engines for millions of people. In this paper, we introduce the phenomenon of data horizons: a critical boundary where algorithmic structures begin to degrade the relevance and reliability of search results. Unlike the core of a data void, which is often exploited by bad actors to spread misinformation, the data horizon marks the critical space where systemic factors, such as linguistic underrepresentation, algorithmic amplification, and socio-cultural mismatch, create conditions of informational instability. Focusing on Tigrinya and Amharic as languages of study, we evaluate (1) the common characteristics of search results for health queries, (2) the quality and credibility of health information, and (3) characteristics of search results that diverge from their queries. We find that search results for health queries in low-web data languages may not always be in the language of search and may be dominated by nutritional and religious advice. We show that search results that diverge from their queries in low-resourced languages are due to algorithmic failures, (un)intentional manipulation, or active manipulation by content creators. We use our findings to illustrate how a data horizon manifests under several interacting constraints on information availability.