After nursing, my 2.5 month old sucks his fingers and occasionally gags himself. why could this be?

A young baby habit: Babies often like to suck on fingers, nipples, or pacifiers for comfort. A baby doesn't know that a finger will go too far down and gag him. With time, he will figure that out and stop gagging himself. If he is doing too much gagging, using a shirt with a sleeve end that covers the hands may help, until he's a little older. Parents can discuss this with the doctor at the baby's 3-month check-up.

Suck/gag reflexes: All newborns have a sucking and a gagging reflex. They have the need to suck to soothe themselves and of course to feed, and the gag reflex to protect them against aspiration.

Not to worry!: There's a fancy medical term for everything, and this one is "non nutritive sucking!" certainly a primitive survival reflex, as is the gag reflex. Because of your infant's age and relatively immature central nervous system, it is not surprising that he occasionally gags himself. I wouldn't lose any sleep over it.