In this paper, we use Formal Concept Analysis to carry out a comparative analysis between the adverse effects present among the vaccines that were applied massively in Mexico during 2022. FCA allows us to reveal relationships between certain vaccines and certain groups of vaccines through shared core properties: Specifically, we discover connections by the fact that every common (positive or negative) side effect of the group also appears with some specific vaccine under consideration. We also investigate a relationship between the ability to neutralize antibodies and the efficacy of the vaccine. Moreover, we construct a more comprehensive concept lattice considering only vaccines applied in Mexico combined with positive and negative side effects and taking also into account the technological platform on which the vaccines were developed and their dosage.