Alternator 13.87 battery charge. Do i need new battery or alternator?
That’s normal output for an alternator.
So it’s not the alternator.
How old is the battery? I’d charge it and have it tested.
The Alt output is fine… make it try to charge a dying batt long enough… and it wont be.
Right now, the OP just needs a new battery. But, the longer that he allows his alternator to work overtime trying to charge the old battery, the greater the likelihood that he will also need to replace the alternator.