Hi R.!
The Binky is not actually a necessary part of babyhood. Some babies want it, some don't, and that is ok.
The pacifier was designed to allow a baby to comfort suck without mom breastfeeding or trying to hold the bottle for a baby who doesn't actually want to eat. It's a convenience for mom, that's for sure! Some babies will comfort themselves in other ways however, and as they get older they depend on comfort sucking less and less. In fact, when a child is about 4 months old, they have lost most of the newborn reflexes and have started getting more control over their bodies. The need for comfort sucking past 4 months declines as they learn to roll over, reach and grasp, and as they become more aware of their environments.
Sucking on his thumb/fingers is what calms him at the moment, but it won't always be so. Most children outgrow it before their first birthday.
Also, if he is teething, his mouth hurts. Talk to your pediatrician about giving him tylenol when he's uncomfortable. In the mean time, by some teethers. They go in the freezer give the baby something cold to gum. The coldness helps numb the gums so they don't hurt so bad during teething.
Good luck, and enjoy your baby! :)