Vaccination provides the best protection against the increasing infections of SARS-CoV-2. The magnitude and type of anti-SARS-CoV-2 vaccine side effects (SEs) depend on parameters that are not fully understood. In this cross-sectional study, the associations between different anti-SARS-CoV-2 vaccine SEs and age, sex, the presence of chronic diseases, medication intake, history of allergies, and infections with SARS-CoV-2 were investigated. Our survey used the Google platform and had 866 participants, contacted through e-mails, social media and chain referral sampling (margin of error ≈ 4.38%, 99% confidence). More than 99% of the participants received the BNT162b2 and ChAdOx1-S vaccines. Being female, having chronic diseases, taking medicines routinely and the presence of a SARS-CoV-2 infection (p < 0.05) were associated with strong SEs after the BNT162b2 vaccine second dose. Having a history of allergies and a female sex (p < 0.01) were associated with strong SEs after the ChAdOx1-S vaccine second dose. Furthermore, the results reveal, for the first time, the associations between having a history of allergies, chronic diseases, medication usage, and SEs of a strong magnitude for the BNT162b2 and ChAdOx1-S vaccines. Additionally, this study supports the association of the female sex and infection with SARS-CoV-2 with an increased potential of developing stronger SEs with certain anti-SARS-CoV-2 vaccines.