Go to a doctor
No, you can't die from an ice pick headache. You can go to your doctors office and get some medicine for the headache.
Ice Pick Headaches are typically treated with anti-inflammatory medications. Some patients find that taking a preventive for them will also help.
An icepick headache is also called a "Cluster" headache. It's very dangerous and considered the worst pain known to medical science. Women who have it say it's a lot worse than childbirth. It's treated as a medical emergency if you're forced to a hospital.
Could it be TMJ? The pain is similar to the pain of an imflamed ligament. I've had both, and there were some definite similarities. One cause is Pseudotumor Cerebri. Also called Idiopathic Hypertension. Go to http://www.revoptom.com/HANDBOOK/SECT53a.HTM for more.
You may be describing Primary Stabbing Headache. Also called Ice Pick Headache, or Jabs and Jolts, this type of headache feels like you're being stabbed with an ice pick. It is usually of very short duration - seconds or minutes. Another possibility is Cluster Headache. These are excruciatingly severe and although of short duration of minutes to hours, tend to come in bunches or clusters. These can be so severe that they are nicknamed Suicide Headaches.
get medicine
You treat a cow by poking it with a needle with a syringe attached filled with medicine (penicillin, oxytetracycline, fluorofenicol, or whatever), not with a bloody ice-pick. That's animal cruelty if you intend on doing such an idiotic and down-right foolish act like that.
Ice-cream treat
The remedy for headache and dizziness depends entirely upon the cause for the symptoms. A headache specialist is the best person to diagnose and treat headache disorders.
If the neck pain is causing the headache, this is called cervicogenic headache. If the headache is causing the neck pain, treating the headache will also treat the neck pain. Pain Management Specialists and Headache Specialists are the doctors best suited to treat these types of headaches.
It treats a bad headache
The treatment for your headache depends on what type of headache it is (there is a long list of different kinds of headaches) and what has caused it. For best results, consult a headache specialist who is trained to diagnosis and treat headache disorders.