cough with rash can be chicken pox but lots of other viral infection may also present with that.so dont stamp it with chicken pox.also chicken pox presents with fever which you have not mentioned.so with the symptoms you are suggesting chicken pox is unlikely.it may be other viral illness.get an expert consultation.yeas adult and youngs are susceptible to it.all those exposed must be vaccinated within 96 hrs of exposure.

Thanks for posting on HCM. The rash of chicken pox is vesicular (fluid filled) and is mostly seen on head, neck and body, upper limbs. The rash is susequently transformed into scabs. Your query does not carry the description of the rash but certainly this information would be helpful to you to rule out the disease in your child.
Normally, it is beleived that a person who had chicken pox in the childhood is immune to it for the rest of life, but there are cases with chicken pox in adult even if they suffered in their childhood, although the chances are much less than those who have never suffered from the disease.
Regards.