Re: cold, now bloody spitting a loogie :-/
Yes, go to the doctor. If you have 103º fever, it's not a cold. I would suspect you either had the flu or a cold that has turned into a secondary infection (probably sinus).
I have the same thing plus laryngitis. After a week and a half of green snot and no voice, I did go to the doctor. Any mucous that is coloured green is prime for antibiotics.
The blood stuff is probably the mucous membranes very irritated from the cold/infection and constantly coughing or blowing your nose will cause it to bleed even more.
You could try steaming yourself to help rehydrate the membranes. I did everything I know to care for myself, but I got worse. My fever wasn't high, but it was just above normal. It goes up a bit more, but not serious like 103º.
Go and get it swabbed. You could have tonsilitis, and if so, it's probably strep.....you want to deal with it quickly.
Keep us posted as to how you're doing.
Get well soon.