your son is suffering from respiratort tract infection, in this infection skin of throat inflammed and becomes thin so when we cough hard it get easily bleed, so do not worry about blood in mucus.
you can use cefixime
syrup 3.5 ml twice daily with ambrodil plus salbutamol
combination 2.5 ml thrice daily.
is present use paracetamol
plus ibupfren combination 3.5 ml 4 hrly.