Gum Discomfort/burning Sensation Just Above the Veneer, Is This Normal?

Most patients do not have adverse reactions to restoration such as porcelain veneers.  In rare cases, a patient may have an alergic reaction to the restorative or bonding materials, but these usually manifest themselves shortly after placement. 

In your case the sensation involves one of four teeth, suggesting a localized problem.  Issues may include the veneer being placed too close to the bone supporting the tooth (violating the biologic width), excess bonding material trapped under the gumline and causing a local irritation or my favorite, PCKS.

PCKS stands for Pop Corn Kernel Syndrome.  When corn is popped, it's thin outer shell fractures and can be easily caught under the gums.  Like a suction cup, this shard can adhere to the tooth and be difficult to remove.  Dental floss can generally catch the edge and remove the shard.  Similar irritation can result from other food debris getting caught under the gums.

Arrange to see your dentist.  Simple removal of the cement or food debris stuck inthis area may quickly alleviate your symptoms.

In most instances procelain veneers have no problems at all. If the end of the veneer is under the gum it may be causing an irritation or they may have left some cement under the gum.  Could be a varietey of different things.  I would go back to the original dentist and have them check the area