(1) Background: The SARS-CoV-2 pandemic has changed the functioning of Polish health systems. Telemedicine has been developed and access to prescription drugs (Rx) has been facilitated. This study examined whether these changes and the imposition of a three-month lockdown caused Polish people to engage in more self-medication-related behaviors. (2) Method: After the fourth (final) stage of defrosting the Polish economy, an online survey of a quota sample of 1013 Polish respondents was conducted. (3) Results: Almost half of the respondents (45.6%) indicated that they had engaged in at least one behavior associated with inappropriate self-medication during the lockdown (e.g., 16.6% took medication as a precaution, and 16.8% took an Rx formulation without consultation). Some of these people had never engaged in such behaviors prior to the lockdown. Linear regression showed that higher values of a composite (“lockdown”) index of self-medication-related behaviors occurring during lockdown were predicted by greater religiosity and the presence of children in a household. Also, independent samples t-tests showed that people who were afraid for their financial future and people who feared for their health obtained higher lockdown index scores than people not having such worries. (4) Conclusions: Self-medication-related behaviors were more common among Poles before lockdown than during the lockdown (which is unsurprising given that the lengths of the periods compared were hugely different), worryingly, many people exhibited such behaviors for the first time during the lockdown.