What, if any, theories exist relating chronic pain to over medicated
injuries during developmental years?  For example, would a preteen
injury that was medicated over time cause the nerve(s) to produce
additional neurotransmitters in an attempt to get the message through
and thereby 'calibrating' the nerve(s) to send an apparent pain
message for the rest of the individual's life?

I tried researching some info about this topic, but it's a very
particular scenario.  For example, how long a period on some type of
analgesic would constitute "over-medication"?  As far as I know,
individual neurons do adapt to changes in stimuli in the way you
describe, but only on the short term (seconds or minute), not over the
course of development, so I wouldn't expect to see a change in pain
perception in an adult in the way you describe.  I'm still trying to
find some good reference material...

Thank you Andrew, I have tried to find references myself but had no
luck.  Basically I'm wondering if being "over-medicated" (by which I
actually mean taking pain killers for extended periods, months to
years, to continue participating in a sport) causes the neurons to
produce more transmitters in an attempt to get the message through and
what effect that can have on neurological development.

Interesting question. This concept is not mentioned in the field of
pain management. The closest concept to your proposed question
involves the idea of "tolerance" to narcotics. Please see the links
below for more info.
http://www.hscbklyn.edu/ginzler%20web%20site/ginzler.htm
http://www.hscbklyn.edu/ginzler%20web%20site/ginzler.htm