battery light on cold start up

[400 dollar yaris]

Hello all,

Yesterday I noticed my battery light on. I pulled over and got my scan tool out and plugged into my car to see if I could figure out what was going on. The battery was running around 11V. So this morning I cleaned the corrosion off of the terminals and went for a drive. At first no light, but then as I started down the road the light came on again. I tried to do a battery test with my scan tool, but it said the battery needed to be fully charged first. So, I went up to autozone and had them test it. They said the battery health was fine, but it needed charged. Their tool said it was around 12v. So I said ok and decided to head home. Turing my car back on after they tested it, no light. Checked again with my tool when I got home and the battery was reading 14V again. I did a battery test on it since my tool said it was fully charged and the battery health came back normal. The serpentine belt on the car does slip sometimes and squeals but ive never had this issue before. I was thinking that this could be due to the belt getting old and wearing out since it has been squealing for a while. I was waiting until it was nice outside to change it, but I may need to tough it out. It has been about 20 degrees here lately and the last time I replaced the battery was december of 2013. I dont believe it is the battery since both my tester and the autozone tester said the battery was holding a charge. My fear is the alternator, but im hoping that i just need to replace the belt and all will be good. Has anyone else experienced this?

Thank you,
400