Does the prescription drug darvon-n cause rebound headaches?

It can. Any pain medication can cause rebound headache. Especially if you're taking it too often. See medication overuse headache (moh). This includes Ibuprofen and acetaminophen. Darvon and darvocet were removed from the market in the us in nov. 2010 due to concerns about increased risk of cardiac arrhythmias, Acetaminophen overdoses and questionable effectiveness.