So... you are being picky with your teacher but it sounds like your teacher was being a little impatient so, it should have been: no harm - no foul.
But... Well.... Ok... So... technically, there is some matter travelling thru space from the sun to the earth (the solar wind and coronal mass ejections, etc) and this matter does have energy so, yeah, not ALL the energy is radiated, only about 99.99999% of it. Are we happy now?
-
"my high school physics teacher said that heat from the sun reaches earth via radiation and it's a distinct form of energy."
It isn't so much "distinct", it is photons, aka. light. Everything from gamma rays to radio waves... all carry energy / momentum, and all are converted to heat by charges associated with atoms, once absorbed.
"I presented a rebuttal that the sun actually emits infra red radiation and the earth absorbs the radiation and heats up as an effect."
The Sun *also* emits infrared, but the "greenhouse effect" allows visible light from the Sun in, the "ground" converts it to heat, and greenhouse gases will not let the infrared (blackbody radiation at Earth surface temperatures is peaked in infrared) back out to space.
"And because IR is an electromagnetic emission, it doesn't need a medium to propagate."
Same for gamma through radio waves, no aether required.
"The teacher disagreed with me, and after I interjected a few times, gave me detention. So which one is correct?"
The teacher failed to get through your Asperger's, and you failed to listen to someone that knows, and whose only job is to teach you to learn.
"The essence of the teacher's statement was that heat is a distinct form of energy by itself and it gets transferred from the sun to the earth as itself. While my argument was that heat is just the effect of absorbing em radiations and can't propagate as itself."