Thank you for your query,
As you told the dog was sick and irritable before the incident the dog might be having some illness like viral or any other illness.
Yes the biting may be related as the sick animals will be irritable and they bite even in unproved situations.
As your child is recieved ERIG,PVRV,ATS 3000 immediately and on the process of taking the other remaing injections according to schedule, nothing to worry as this schedule will provide full protection if all the rabies vaccination
injections are taken according to full schedule.
You can convey the the death of the dog to your doctor and according to his advise proceed further.
Hope i have answered your query.