I have a ferrous solenoid core coil that is winded 5 layers tightly with the length of the core of 11cm. I didnt expect it to do more than picking up a few paper clips but I hook it up to a 1.5V D battery, it sparks up and shocks the hand at times. What causes the voltage to rise?

 

The solenoid coil forms an inductor which has inductance.
When you pass a current through this inductance it stores energy equal to 1/2 LI² in its magnetic field where L is the inductance in Henrys and I is the current in amperes.
When you break the circuit, the magnetic field will collapse, causing a voltage in the coil to be generated, with the voltage rising to whatever it takes to keep the current flowing until this energy is dissipated.
This can generate a very high voltage across the contact gap when you open the circuit as the current continues to flow across the gap, creating the sparking and the shock you noticed.

That's why arc suppression circuits are often placed across electrical contacts that switch inductive loads, to absorb the inductive energy and keep the contacts from pitting and possibly welding due to the arc that would otherwise form when they open.

If it helps, the mechanical analogy of inductance is the inertia of an object.
Once you get an object moving it wants to stay moving until all the kinetic energy of its motion is dissipated. The more rapidly you try to stop the object the more force it will exert.

 

Also the effect of the very fast collapse of the magnetic field across the winding when you suddenly disconnect the coil is explained in Fleming's right hand rule.
Max.

 

In the early days of internal combustion engines what you experienced was use to provide the spark to make the run, it was known as a 'low tension coil'. Many of the stationary engines used on farms used this method.
https://en.wikipedia.org/wiki/Low_tension_coil

 

A reverse biased diode can be placed in parallel with the coil to allow the current to 'recirculate' as the magnetic field collapses. It should have adequate ampacity.