Battery Trouble

Last night was the night from hell. On the way back home from the mall all the lights on my car started to get real dim. Then my battery light came on. So I pulled off the road to check it out, shut off the car (like a dumba**), and after I checked it out I couldn´t start the car. So my sister and I froze our butts off waiting for someone to show up who could help us. This women pulled up and said she was going to call her husband who lived up the road to help us. She did, but the guy never showed up. So I walked up the road aways and found a house, luckly the guy who lived there was able to give me a jump. After they the car ran fine for awhile and then everthing went dark again. We pulled off at a gas station and decided to call home for a ride; this time I kept the car running. Anyway, as we were sitting there the battery somehow charged up because when I tried the lights again everything was as bright as it was supposed to be. Also with the heater on we could smell burning rubber (the same smell you get when your vaccum cleaner burns a belt.) Anyway I went up today in the daylight so I could drive it home. I´m trying to figure out exactly what is wrong, so when I go to the garage tommarrow I´ll know what to tell them to fix. I have a feeling that the belt has gone bad and is slipping on the alternator. One reason I know this is because it sqeals when you first start the car or if it rains. I don´t think it is the alternator itself otherwise the battery wouldn´t have charged itself up while we were parked. I want to know what you guys think?

(Whew, that was a long one!)