The point is, with the symptoms described how can you tell if it serious or not?
Most likely mermaidgirl is correct, a simple sinus squeeze, it could also be a symptom of sinusitis, most unlikely it could be a tumour of the sinus.
The trouble with posting something wrong with you and asking for advise is most people tell you what they had wrong with them, which is fine if you have the same thing but next to useless or even dangerous if you have something else.
At this moment I'm sat next to consultant surgeon, she says there are at least ten problems that headache and nosebleed could signify, if she can't give a diagnoses from the symptoms, I'm willing to bet no one else can either.
Why take the risk?
Go and see your GP, if it's a simple squeeze, great no problem, if something else,then the earlier the diagnoses the better.
Dave.