You need the normal rather than the angles. You can create two vectors from the two angles as (cos(xangle),sin(xangle),0) and (0,sin(zangle),cos(zangle)) which are both unit vectors and their cross product is a unit normal. Which direction the cross product goes depends upon whether it is a left or right handed coordinate system.

The most straight forward way I can think of to get the new direction is to convert it to a coordinate system in which the collision point is the origin with the velocity and normal vectors within a plane formed by two of the axes, i.e. xy, xz or yz planes. Your normal would be one of the axes. The cross product of the normal with the velocity vector and the normal would give you another once you convert it to a unit vector. The cross product of the normal and that second axis would give you the third axis. That would give you the information to construct a transformation matrix. If you run the velocity vector through that transformation matrix you will get a vector that is in the plane formed by the normal and third axis. If you then reverse the sign of the component of the velocity vector in the direction opposite the normal then you have a velocity vector reflected across the normal. If you run that through the inverse of the transformation matrix you will be back in your original coordinate system.