Help! My 97 Jeep Grand Cherokee keeps dying!

Please. I really need help. Im only 18 years old and I bought my Jeep as my first car in April. About a month ago, a nine-month old battery kept going dead so I had it replaced. Now, problems are returning. A few days ago the engine was slow to start and the lights seemed dim. Yesterday, in my school parking lot it died in the middle of the street out of nowhere and I couldn't start it again. Everytime I did, it just died again. My dad came and gave me a jump and it had a lot of spark and started right up and I drove home perfectly. My mom drove it today and she said it drove perfect, except after she filled up with gas, she went about 20 feet and it died. It started up a minute later, and drove perfect the rest of the day. What could it be? Some think it may be the alternator. Others think it could be floater in the gas tank thats getting stuck. And some think it could be faulty wire to the battery or alternator. If anyone has any ideas, please help me! I don't want to take it in and pay a crapload if its nothing. Reply even if you're not sure. I'm a girl who knows nothing about cars :cry: