What else can I do for ice pick headaches other than use a beta-blocker?

Lots of things. There are many treatments, both medical and nutritional to help with cluster headache or migraine. Decreasing stress, avoiding stimulants such as caffeine and nicotine and avoiding dehydration are a start. Many people get rebound headaches from taking pain medication regularly. These can be severe like a migraine or a cluster cycle headache. Lastly, there are a number of classes of medication.
Oxygen? Ice-pick headaches are another name for cluster headaches. Sometimes typical migraine treatment (imitrex, etc) can help. An old remedy that sometimes works very well is oxygen. Next time you're having a headache, see if your doctor will administer oxygen. If it's going to work, it typically works in less than 5-10 minutes. If so, it can be an inexpensive, easy solution even for home use.