Veneers causing tension headaches and vertigo. What do I do?

Tension headaches and vertigo symptoms can occur when the lower jaw is positioned too far back which puts tension on the temporalis muscles and puts pressure on the inner ear.  I would recommend having your dentist check the bite to see if you can have a bit more freedom of movement anteriorly (forward).  You may have had some bite issues to begin with that were not fully symptomatic and this procedure sort of tipped you over the edge.  If bite adjustments do not resolve the issue, I would recommend you see a neuromuscular dentist in your area. 

It's impossible to answer your question without more information to get a diagnosis of your headaches. I suggest you consider getting a second opinion and possibly visiting a neurologist. There are many causes of headaches. It may be circumstantial and not related to your veneers. If the headaches are determined to be directly related to the veneers I'm sure the dentist would love to discuss options to take care of your problem.