Can sneezing violently multiple times in a couple of minutes do any damage to my eyes or nose?

Probably not. Violent sneezing (or coughing) can increase the venous back pressure of the eyes and cause hemorrhage under the conjunctiva and sometime in the back of the eye (subretinal). This effect is more likely with vascular fragility for instance in diabetics. However. Millions sneeze, cough and lift heavy weights with no problem - not that you can easily stop the sneezing to begin with!
Avoid violence. Don't hold a sneeze in--let her rip!