Could you ever have an allergic reaction to a bee sting several days after a sting?

Yes, differ manifest: Immediate reactions, ige antibody mediated, are the ones associate with dangerous anaphylaxis (airway obstruction, blood pressure drop, wheezing , hives). Delayed reactions tend to behave differently and have different mechanisms. They tend to be more likely rashes, delayed swellings. Sometimes there are fevers, joint aches but these resolve over time.