That's it. The one on the left. It had a pinhole in it a couple of inches from where it conencted to the heater core. When I went to get the hose I was given the "rubber" heater hose part. I cut that leaking section out and replaced it and clamped it on both sides.
Now (week or so later) I smell a strong hint of coolant with my heater on. Could I have damaged the core and caused another problem? I do know that the original problem (the burning cooland smell) was due to the pinhole because I could open the hood and see it squirting). The smell went away but now the coolant smell from the heater is there. There is no fog from the heater and there is no puddle under the car of coolant.
Where did I screw up?
Thanks for the help and the pictures. That is above and beyond. I do appreciate the help.