Best Answer: I know sinus infections can cause horrible headaches, but not nose bleeds. High blood pressure can cause headaches, dizziness, nose bleeds. Dry winter air can cause nose bleeds, and a headache. Another cause could be from severe nose picking, that can cause horrible headaches and nose bleeds.Blowing your nose too hard can cause a very bad headache and a possible nose bleed.But any combination of a headache and nose bleeding consistantly would warrant a visit to your health care practitioner.lowing your nose too hard can cause a very bad headache and a possible nose bleed. But any combination of a headache and nose bleeding consistantly would warrant a visit to your health care practitioner.