Hi,
Continuous cough can make small cuts inside an irritated throat and sometimes little blood can come out along with mucus. You should control the cough with some cough syrup and the blocked nose can be easily cleared by inhaling medicinal vapours like Vicks VapoRub.
Solace
You should definitely see a doctor. Even with a severe cough, it would be very rare to see any blood. You should let your parents know about this if you haven't already. I'm not sure where you live, but tuberculosis is still possible to catch in school in some parts of the country, and is likely if you have also had a fever. Best to get checked out as soon as possible.