My 8 yr old son has been sick with a fever, headache, dizzy and lightheaded for a week. Now he is getting nosebleeds after dizzy spells. Could this be something serious, or just really bad sinus?

See an ENT. Hard to tell what is causing this without more information - is your son athletic? Is there a family history if this? Also, he needs an ENT to scope his upper nasal passage and airways to find an etiology to the nosebleeds. The ENT may want some imaging of the sinuses prior to endoscopy to see the anatomy...
Yes. It could be something serious. Your son needs to see a Physician...now.