my son is going to be 4 months old. these few weeks, he keep licking his fingers on both his hands and sometimes lick so vigorously that it looks like he want to put his whole fist in his mouth. i let him be because i didn't want him to be use to pacifier. however, he didn't cry as you mentioned..
i thought he is teething too. his saliva flows out a lot which is similar for teething children. but the signs of teething stops there... so i dont't think he is teething now.
Baby Teething - Symptoms, How to Ease the Pain and Much More!