The diagnosis has to be made beyond a shadow of a doubt prior to a drastic step like prolotherapy. You must make sure you are absolutely sure of your diagnosis. Weakness of the C1-2 ligaments is generally only found in patients with Down’s syndrome or Ehlers Danlos disorder.
Remember that prolotherapy is essentially a destructive procedure where a toxic chemical is injected into the area being treated. This chemical is designed to cause injury and the healing with scar tissue (which is rigid and contracts). This is what the prolotherapist is after. This injected chemical can injure structures and the C1-2 area is full of structures that when injured can cause devastating consequences.
You should look long and hard about this. I would not recommend it.