A child who has had an allergic reaction to amoxicillin should avoid any medicine ending in cillin to be safe? or anything that contains a cillin?

Depends: Some allergic reactions like a simple rash are more cosmetic than worrisome and not as important as major hives or swelling of lips and difficulty breathing. The more intense the reaction the more important it is to avoid the trigger group. If a cillin med were the best choice in a major infection, an allergist could do some specialized work to desensitize the patient and make use safe.