What is that white pigtail connected to these wires?
I have 2 14-3 wires circled and need you to confirm but believe I understand what’s going on:
Wire 1:
Is the black wire if this Romex hooked up to the second switch in this box that you sat is the ceiling fan? It’s hard to tell from the picture. If so follow along below, if not let me know and don’t follow 
Again assuming that black wire of Romex 1 is hooked to your ceiling fan switch:
- this Romex is your load to the ceiling fan, black wire is your fan and red is your light
- this means you have line and load in this gang box and your wiring needs adjustments
- the reason the red of this wire is connected to the red wire of Romex #2 is because that was load being sent to your other switch box.
- Remember dumb 3 ways have to have load and line split in different boxes
- This is also why your light doesn’t come on unless you have the red and black connected on your Aux switch because that wire terminal is basically connecting the black and red wires together which sends power to your light.
- I hope you didn’t fry your Aux switch by connecting these wires to it, but I do know these GE switches use 120v for the traveler anyway so you may be ok.
Wire 2:
- this is the 14-3 wire that goes to the other gang box with the aux switch
- the black wire is not the load as you thought and it needs to be capped as it’s not needed.
Here is what needs to change:
Master Switch gang box:
- disconnect the red wire bundle
- The red wire of Romex 1 is your load to the fan light so connect that red wire to the load terminal on your master switch
- the other red wire from Romex 2 will be the traveler to the Aux switch so connect that to the traveler terminal on the master switch
- put a wire nut on the black wire of Romex 2, which you currently have hooked to the load, as you don’t need it
- keep your white wire pigtail going to the neutral bundle in place but make sure the white wire from Romex 2 is also hooked up to the neutral terminal so we can “send” neutral to your aux switch
- you can turn power back on at this point and verify that your master switch turns on the light.
Aux switch gang box:
- assume there is a 14-3 wire, red, white, black, where all wires are hooked to your aux switch at the moment
- put a wire nut on the black wire as that is no longer needed
- hook up the red wire to your traveler terminal
- hook up the white wire to your neutral terminal
That should do it
Later if you decided to smarten your fan, remember that the black wire of Romex 1 is your load.