I'm going through the same...I went and bought some dove deodorant that supposedly clears up the darkness because I was so freaked out...lol but I learned that it should go away
Lemon juice or Lime juice
It's totally normal. :) It's called hyper pigmentation. The most common sights are the inner thighs, middle of the belly and armpits. It's caused by the increase in estrogen. Sunlight can make it worse so, careful with the tank tops. Since you have noticed it under your arms,be prepared to see it on your face too. Then it's called melasma. Neither is permanent. It usually clears up on its own after delivery. :)