Yes, check it at the battery (m)
14.53 is a bit on the high side possibly because you may have a bad connection somewhere, or an alternator is only working part time which could explain why your battery dies.
When the alt light comes on it's not charging the battery either because the alt is bad or the fuse for it is bad. Since it works most of the time I would have to guess the fuse is OK.
Next time the alt light comes on, shut off everything you can that uses electricty. You should be able to drive ~30 miles before the battery dies.