Will my son's strange reaction following antibiotics last.

No. Most children who use antibiotics do not get any reaction. Kids who do get reactions may get rashes, nausea, diarrhea, or vomiting (other reactions are uncommon). Reactions usually go away shortly after the antibiotic is stopped. Any child who has some sort of "strange" reaction should be evaluated by a doctor.
Yes or no depends. What does this reaction look like and feel like. Was he in the sun has he had drug allergies why was he taking antibiotics there are a number of severe reactions that can occur as well as mild relatively harmless ones due to a lack of information play it on the cautious side and have a doctor take a look.
Yes. Allergic reactions to antibiotics, ie hives can last up to two weeks after stopping the medication. Antibiotic induced diarrhea can improve soon after discontinuing the antibiotics or linger. There are other nonspecific rashes that are not an allergy but an interaction between the antibiotic and a virus that can last for days. Behavioral reactions to colorings or flavors abate qickly.
Maybe. It is unclear what you mean by "strange reaction." antibiotics mess with the bacteria that live in everyone's guts. These bacteria are part of both the immune system and the digestive system. Changing these can result in changes in digestion and immunity. Problems like these, and maybe your son's problem, can be prevented and/or improved greatly by daily probiotic supplements and foods.