Interesting that an antibacterial cream would be good for something like that. It doesn't look like an infection.
I've used antibacterial cream for skin issues in the past where it was a known bacteria infection, things like an abscess, but I would not expect that kind of cream to help for something like that. But if it works, great, and no point in questioning it. Just carry on until it's gone. Shouldn't be that long if it's working.