Hi - Well, I can't say with any certitude that it is columnaris... If the lesion is bulging rather than indurated it might be something else... but if it spreading, that stillpoints to infection. I would go ahead and try antiobiotics - those are all pretty broad spectrum so whichever one you chose might do the trick - if it doesn't respond to one or two different antibiotics, you may have a tumor on your hands.
I never did figure out what Fafner had but the sulfa antibiotics (I used Maracyn Plus) definitely cured him. He had a white pustule-ulcer type thing in his face that spread to his eye and eventually gave him popeye... It did not match a description for any Betta diseases and believe me, I looked! But, luckily, the Maracyn Plus worked.
I agree with Chishower that unless the other fish starts showing symptoms, you may not want to give it antibiotics - resistance makes them much harder to treat next time... Hopefully, the other Betta will be OK - maybe a nice big water change!
Some fish are just stronger than others - so your other Betta may just have a stronger immune system, you never really know (I'm still trying to figure out what happened to my frog!

b/c the other one is perfectly fine!)
Hopefully, I did not insult you with any obvious basic advice on Betta care, but you'd be surprised what some people do - so I just thought I would make mention of - I knew of a patient once, allergic to his dog, he got asthma. When asked how his inhaler was helping him he said it did not have much affect - no one could figure out why... Finally, someone said show us how you are using the inhaler and he said - I can't becasue I did not bring my dog with me! Whenever he had an asthma attack, he sprayed the inhaler on the dog!

(This is a true story)! So, I just thought I would mention it just in case... but you seem to have your head screwed on tight!
I hope you fish heals soon!
PS - I can send you some medicated food if you want to try a little...
Chishower - i like your new avatar! I was really well-read up lately since Fafner was sick last week. None of my other Bettas ever got sick! So, I had a lot to learn!