Recess light not working
Your explanation is confusing.

However, the one thing that stands out is you said you connected the black of the light to BOTH of the blacks in the cable AND the red.


  Hooked up black of light to black of both 14/3 and 14/2. Hooked up red (switch hot?) To black of light.


A device can only be connected to one wire that is either always hot or switched. You have apparently connected the light to all three hot wires in this circuit.

You need to study standard electrical wiring diagrams a little more and check your wiring again.

Good luck!