A few things that can erupt are : anger, volcano, tooth, rash, riots, unrest, etc. Erupt has several meanings.

  Their explanation, with examples, is given as follows:

(1) Start unexpectedly
Example : Riots erupted in the city.

(2) Start to burn or burst into flames Example : The spark soon erupted into flames.

(3) Become active and spew forth lava and rocks
Example : The molten lava erupted out of the active volcano.

(4) Forceful and violent release of something pent up
Example : The difference in their views soon erupted in a fight.

(5) Sudden appearance on the skin Example : On the day of the party, a pimple erupted on her face.(6) Break out
Example : Eruption of the wisdom tooth gives a lot of pain.

Things that can surge are : pride, anxiety, waves, boats, army, etc. 

The several meanings it has can be explained with the following
Examples :

(1) Sudden forceful flow
Example : The boy drowned in the surging waves.
(2) Rise and move forward
Example : The army surged towards their enemy.
(3) Heave upward under the influence of a natural force Example : The boat surged in the high tide.
(4) See one’s performance improve Example : Hard work helped to surge Sandra’s scores.
(5) A sudden or abrupt strong increase
Example : The surge in the stock market left people in a shock.
(6) Rise rapidly
Example : As time passed, her tension surged.