I know that when two particles are collided some new particles come into existence and i know that the new particles weren't inside of the original particles.
Yes, there is extensive experimental evidence for this.
I understand that the energy of the collision can vibrate other fields to make particles.
The standard model of particle physics which describes with great accuracy the collision and predicts the future behavior is a mathematical model based on quantum field theory.
Each elementary particle in the table is assumed to be a field permeating all space, like a coordinate system. This field is mathematically represented at each (x,y,z,t) by the free particle solution of the corresponding equation,(Dirac for fermions for example). On these solutions creation operators ( differential operators) create a particle and annihilation operators destroy it. In this way a propagation, a "track" for an elementary particle can be envisaged, using wave packets with the appropriate energy and momentum and heisenberg uncertainty.
When two particles interact, the theory has specific rules which were developed to fit and predict the data, and are simply described for calculational purposes by the use of Feynman diagrams.
The energy of collision can allow creation operators to work on the underlying fields and create new particles which will propagate away from the collision, as long as energy, momentum, angular momentum and all quantum numbers that have to be conserved are respected.
Not vibrations, but creation and annihilation operators acting on underlying all permeating fields is the mathematical model which succeeds to describe the data.