Should I stay up overnight to keep an eye on my 3yr old after allergic reaction? She had lip swelling and was prescribed antihistamines.

Do not have to. Now that it's under control and you do not use the same substance that caused the reaction, it should be ok.
You should not . Have to. Continue giving the antihistamines as prescribed unless with respiratory symptoms, shortness of breath , then you need to be concerned.Take him to the emergency asap. Follow up with your pediatrician to see if there is need to refer your three year old to the specialist.