706 is exactly right. As someone who has made thousands of gallons of hard cider and apple wine, let me assure you that, given the descriptions you gave, esp. the puffy jug (!! which most certainly ¡whooshed! a bit as you took the top off), your sweet cider has undergone alcoholic fermentation. Look to see if there are any preservatives listed on the label--I suspect not.
If it's been in the fridge the whole time, it most certainly is still actively fermenting. Pull it from the fridge, put it in a cool--not cold--place, with a paper towel or section of cloth rubber-banded/affixed totally across the mouth. Wait a few more days. Back in the fridge, chill, pour very carefully (there'll be debris in the bottom of the bottle), and enjoy!
The chances of something bad happening to a fresh, clean sweet cidre instead of alcoholic fermentation are microscopically small.
Geo
Sooo, you like wine and are looking for something good to read? Maybe
*this* will do the trick!