that sound like the alternator to me, unless you have a wiring problem, which i doubt (if the alternator wiring is faulty, it may not be charging you battery properly).
If you have a voltmeter, check battery voltage with car off (should be 12.5V), then check again with car running (should be 14V +). If you don't have a voltmeter your dash gauge will give you some indication. if the voltage appears low (below the half way point), then the alternator is not working properly.
If you have a stock alternator, you can purchase a re-build kit for around $20 - and its simple to do. the re-build kit comes with new brushes (which it problably the problem with your alternator, and it also coes with a new voltage regulator) the brushes are 2 rectangular pieces of soft metal which rub against the spinning rotor and produce electricty. these brushes will wear completly down within 5-10 years. You can buy and replace just the brushes, which cost around $3.