COVID-19 pandemic-related perceived risk of infection, illness fears, acute stress, emotional anxiety, exhaustion, and fatigue, psychological trauma and depressive symptoms, and sustained psychological distress can cause smartphone addiction risk and lead to technology-related cognitive, emotional, and behavioral disorders, thus impacting psychological well-being. Behavioral addiction of smartphone users can result in anxiety symptom severity, psychiatric symptoms, and depressive stress. We carried out a quantitative literature review of the Web of Science, Scopus, and ProQuest throughout June 2022, with search terms including “smartphone addiction + COVID-19” + “stress,” “anxiety,” “depression,” “psychological distress,” “screen time,” and “fear.” As we analyzed only articles published between 2020 and 2022, 288 papers met the eligibility criteria. By excluding sources with similar titles, having unclear findings or unsupported by replication, or displaying inconsistent content, we selected 64, mainly empirical, sources. We used layout algorithms (VOSviewer) and bibliometric mapping (Dimensions) as data visualization tools. Assessing the Methodological Quality of Systematic Reviews (AMSTAR), a systematic review and literature review software (Distiller SR), Mixed Methods Appraisal Tool (MMAT), and Systematic Review Data Repository (SRDR) were employed as methodological quality assessment tools. As limitations, we analyzed only articles published between 2020 and 2022 in scholarly outlets indexed in the Web of Science, Scopus, and ProQuest databases. The scope of our study also does not advance the inspection of sources covering vulnerable individuals suffering from certain diseases or specific generations. Subsequent analyses should develop on smartphone use and addiction among children and adolescents. Future research should thus investigate problematic smartphone use and addiction across generations Z and Alpha. Attention should be directed to their personality traits and psychopathological symptoms.