You should definitely see a doctor. Maybe you could get in to an urgent care clinic since it is the week end. It could be a sinus infection, bronchitis or many other things.
I know spitting out blood is scarry. Been there and done that. My GP was not overly concerened, but did say I needed antibiotics. I will be discussing this further with my asthma doctor at my next apointment.
You had sore throat since past 2 weeks but you did not take treatment for that I believe. Do not worry, probably because of forcible sneezing or because of your sinusitis problem you had bleeding from the nose. Any way, you need to get it examined from your ENT specialist. Till then try saline nasal drops so that it keeps your nose moist and reduces the bleeding from the nose. Drink plenty of warm water. Any more doubts you are welcome.