Antihistamines. Allergic reactions to stinging insects include symptoms distant to the site. It includes hives, generalized redness and itching of the skin, asthma symptoms, and the most severe is an anaphylactic reaction. Local swelling the next day is not uncommon, but one needs to watch for signs of infection. Ice for the first 24 hours, elevation and then local heat.
Ice and benadryl (diphenhydramine) A bee sting can cause immediate fear and panic, and sometimes with good cause. However, by the next day, if there was going to be a bad reaction it would've happened already. What you have is a by-product of histamine release, which causes capillaries to get leaky and allow fluid to seep out. The swelling can look cartoonish, but it will go down. Apply ice and take benadryl, (diphenhydramine) which helps over time.