Hi, and thanks for your medical question on eHealth forum
With a history of sore throat, swollen glands and bloody nose EBV infection or mono should be looked at.
The other thing is that you are coughing up blood. This can be due to bronchitis or pneumonia, lung cancers (especially in smokers), tuberculosis, bronchiectasis, pulmonary embolism, or fungal and other infections.
Discuss these possibilities with your doctor. It is difficult to comment beyond this without examining. A comprehensive investigation is required keeping all the points in mind. Hope this helps. Take care!