Battery and Alternator
It could be that the alternator you bought was in a weakened state.
About a year ago, my wife called me after seeing 'Christmas tree lights' appearing on the dash. She got herself to the destination, but the battery died. I purchased a replacement battery and showed up to install it, but the bolt holding the battery bracket was rusted, so i couldn't get it out until the next day (I was able to jump it and get it home). I put the new battery in and thought everything was fine, for about a week. Then on Christmas Eve, I was driving the truck and saw the 'Christmas tree lights' (died in the Ford dealership parking lot). What happened to me was that the new battery was too strong for the weakened alternator that worked harder than it should have had to for a period of time (the battery was 11 years old). I had the alternator replaced (no issue going cheap by the way, because this Christmas Eve fix was over $550 dollars).
You spend what your budget allows you, but keep in mind that unless the yard has a limited return policy, you might be better off going a step deeper than you might have wanted to. Otherwise you might be rolling the dice a bit. If it wasn't Christmas Eve and I wasn't relying on the truck, I would have bought a rebuilt alternator and done the repair myself. Good luck on the repair.
Kevin