By the description given,it appears that the infection has invaded the pulp of the tooth. In such cases,there are two options,get root canal done which is usually followed by a crown(cap) or extraction of the offending tooth followed by a space maintainer. However,wherever possible root canal treatment is a more favorable option as a natural tooth is the best space maintainer for permanent teeth.
Next Steps
You should take your child to a pediatric dentist/ pedodontist.
Health Tips
Do not scare your child with threats of injection.