I had the same problem, has occurred twice in last 4-5 years.. first time was mild and did heal itself, but this time, was under both arms and really quite irritating...
tried various solutions, from anticeptic creams to e45 cream..nothing... then tried kiehls nappy rash creme, and within hours it felt different..lines remained for another 2 weeks-
believed it was a deodorant reaction, so tested the deodorant again, and flared up within minutes, so painful this time, so replaced kiehls with a chemist standard nappy rash creme, and within 4 weeks both armpits are totally clear.
Hope this helps,
Anthony