Alternator/Battery wiring issues

Hello, I have the car listed above Touring Edition. I was driving home and the information center on my dashboard showed "battery not charging." About a mile later, the dashboard lights and headlights went dark. Then I lost power in the engine. I noticed that I had a black wire from the negative side of the battery cable had come loose from the back of the connector. I got the car jump-started and it fired right back up. I revved the engine to see if it was going to stay running. It did from that point until I got about a half mile. Then the same message as before and it shut off. Long story short, I'm wondering if I did the right thing by changing the battery. Then I got a new battery in it, started it and drove with my dash stating I had started out at 14.6 volts. Before I went the mile and a half to my mother's house, the same thing happened with the dash and headlights, when I only had the fans and defroster on with my headlights. Noticing the entire time, I was losing voltage, down to about 10.3 volts. What are your thoughts about me being able to fix this myself and how much is it going to cost me? Thanks in advance.