Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
There are several causes of headaches. Headaches can be divided into primary and secondary. Primary headache disorders are headaches without a direct cause. These are diagnosed after secondary causes have been excluded. Secondary headache disorders are due to an underlying problem, there are many many causes but some include medication side effects, systemic illness, nervous system infection, tumors, bleeds in the brain or clots in the veins of the brain, and others. The latter disorders are best investigated with brain imaging (CT scan, MRI) or other tests as indicated.
Primary headache disorders are much more common than secondary ones. There are several primary headache disorders. For example migraines, which usually a pulsating throbbing one-sided pain with nausea and discomfort in bright lights that lasts several hours. Another type is cluster headaches, which you mention above, which are sharp pains that occur around and behind the eye often at night and are associated with tearing of the eye and running of the nose. Cluster can sometimes be confused with another type of headache called paroxysmal hemicrania. This is marked by episodes of stabbing or sharp pains that occur on one side of the head and may be associated with eye tearing or runny nose. The difference between paroxysmal hemicrania and cluster is that cluster most often occurs during the night, wheras with paroxysmal hemicrania, episodes occur during the day. The treatment is very different, so a correct diagnosis is essential. Before either of these diagnoses is made, imaging of the brain is indicated to exclude a secondary cause.
Continued followup with your physician is recommended, with referral to a headache specialist (a neurologist specialized in headache medicine) as indicated.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.
I'm not a physician but I'm wondering if the nasal discharge is spinal fluid. I think you should consult a neurologist ASAP.