it's possible, but it's also possible the battery is completely shot and won't accept a recharge. there are ways to test it yourself, but if you know nothing about cars or electricity, best thing IMO is to get the car to autozone or advance auto or o'reilly etc. -- they will hook up a machine to the car for free that can tell you if it's the alternator or battery.
you can try putting the battery from another car into yours, and putting your battery into a car you know works fine. if your battery is bad, the other car won't be able to recharge it either (it'll also die after you jump it off). if your alternator is bad, your car will use up the charge in the 'good' battery too - your headlights will keep getting dimmer and the car will eventually die.
sounds like your family is good to help you! isn't that a blessing?!
good to hear.