So this statement is essentially correct: "heat from the sun reaches earth via radiation and it's a distinct form of energy." But in physical science terms "heat" is not the best word here. I would use "Energy" Radiation is distinct form other forms of energy and it is the only way the energy of the sun reaches earth.
This statement is essentially correct: "the sun actually emits infra red radiation and the earth absorbs the radiation and heats up as an effect." - But it really does not differ fromt he teacher's statement, other than being over specific about the specific part of the spectrum (which actually reduces the correctness of the statement)
Now you get into the weeds: "And because IR is an electromagnetic emission, it doesn't need a medium to propagate. The teacher disagreed with me, and after I interjected a few times, gave me detention."
You are correct in the IR is EM and does not need a medium to propagate, but you seem to be suggesting that the teacher's use of the term 'radiation' did not refer to EM and was somehow an assertion of some other energy transfer like convection And on that point you are just wrong.
Edit: In the Physical sciences "heat" is a distinct 'form of energy' from which one can derive power. So heat or heating (the transfer of thermal energy from a warmer source to a cooler one) be it from radiation, Conduction, or Convection is a distinct form of energy from which to draw power. So yes, from that perspective 'heat' is a form of energy and as your teacher said that particular transfer (from sun to earth) occurs by radiation. So your teacher is still correct, you are only wrong in not understanding the difference in the 'form of energy' concept and the propogation method - but quite possibly your teacher did a lousy job at explaining it.
http://en.wikipedia.org/wiki/Forms_of_en...