Could I be allergic to Lumineers?

Allergies to porcelain ( which is inert material ) is rare, All porcelains are different in their structure!
Although lumineer or veneer are said to be made of porcelain, the molecular structure of each porcelain varies significantly. Patients can be allergic to zerconia (lava) or lithium disilicate (emax) which is categorized as porcelain when in fact they are metals but white!
Allergies to dental materials such as impression material, dental cements, plastic material, composites for bonding, local anesthetic and metals are not uncommon. Although there is allergic testing to dental materials, such as Clifford testing, I have found that to be inaccurate also!
Be aware that one should distinguish between allergy (swollen tissue, runny eyes, and etc...) and inflammation due to bacteria. So best is to check with your dentist to make sure there is no infected tissue first, if all is ok, then yes there is possibility of allergy to the new material used by your dentist. 
The dentist can ask the laboratory to provide the exact material used, and you as patient can get allergic testing to that material. Although this is lengthy and costly period  the patient needs to go through at the end it is all worth it! If you are not allergic to that material then the next step gets harder, since the dentist must now provide one by one each materials used in conjunction with the cementation procedure to be tested individually, to find out the solution for patient! 

It is possible to be allergic, but also highly unlikely. Perhaps you should investigate if there is an infection or foreign body reaction. 
Best,

This would not be my first thought. I have had several patients who remained swollen for a period of time after dental treatment due to a sensitivity to the anesthetic. There are other courses of treatment to reduce inflammation . Ask you doctor for a prescription antiinflammatory.