Any such thing as a delayed allergic reaction to a bee sting?

Bee sting allergy. Venom does not cause a delayed reaction, it causes an immediate reaction. What you have is undoubtedly an infection. Whether it is an infection that requires medical treatment, or one that you could treat yourself by applying a topical disinfectant like tincture of iodine. If a reaction continues see you local doctor.
Yes. Allergic reactions usually occur within minutes to an hour after a sting rarely the reaction can occur as long as 24 hours after a sting. Infections at the sting site can occur but this would not be an allergic reaction. Evaluation of the reaction by your physician or an allergist may be needed. I hope this helps.