Not specifically cockroaches all allergic reaction present as cough rash difficult breathing   asthma like condition

nothing speific about cockroaches. Symptoms are same as of any other allergies, Asthma ca become worst, common cold is very frequent. But there is way to diagnose it . Patch test to protein in cockroaches Treatment is also same , and specific treatment to clean up house , corner, of any drawers. you can keep some repellant, like bay leaves can act like repellant

He will get repeated cough, wheezing, cold, sneezing, itchy eyes, red eyes. You can prevent it by pest control only ( do herbal pest control)