If ibuprofen is no longer working to reduce the pain from a toothache, would dihydrocodeine be a good alternative?

Depends. Without a complete medical history and a diagnosis of what is causing the dental pain, you are self prescribing. Not a wise thing to do without knowledge of drug interactions and a diagnosis as to the cause of the pain.
Not for long-term. What do you propose to take when the Codeine does not work? This is a losing battle you are fighting. The pain is caused by a problem. The best way to make the pain disappear is to address the problem by seeing a dentist. I realize that it is sometimes difficult to visit a dentist, but if you don't address your dental problem, it will likely not resolve itself and will likely become worse.
Perhaps, but. Perhaps, but does not solve problem. See DDS for cause - treatment.

Related Questions

If ibuprofen is no longer working to reduce the pain from a toothache could dihydrocodeine be effective?

Better Direction is. The better option is to take 1-regular Aspirin tablet with 1-tylenol tablet. When taking either of these, do not take any ibuprofen.
Another option. Pain medications serve only to help manage the perception of the pain, but rarely will address the cause. If there is a progressively worsening pain, you should seek the care of a dentist and have the offending tooth treated. To answer your question... The combination of Ibuprofen (600 mg) with an opioid medicine (like hydorcodone with tylenol) is a quite effective protocol.
Better solution. Toothache is your bodies way of telling you that you have an untreated infection. You can mask symptoms with analgesics, or reduce severity w antibiotics, but neither will "cure" the infection. You may need filling, root canal treatment and crown, or extraction and replacement. You can cll dentist now for emergency visit or you can wait until the pain gets overbearing and the infection spreads.