Armpit swollen lymph nodes caused by shaving.. how long it'll take them to go away?

Difficult to say: There are several things to consider. It could be just run of the mill mild folliculitis...But there is also something called hydradinitis supperativa. The latter is more acne like and takes far long to treat and go away. For now..Stop shaving. Make sure you replace the razor frequently and sterilize it in chlorox or the like in between shaves.