Correct, alternators don't fix themselves but can fail as your is.

Can also be a failing regulator.

You can check the alternator at the battery terminals with the engine running.

For grins, check the battery terminals to verify they are tight and not corroded and load test the battery even though it is taking a charge. Autozone or other auto parts store can load test the battery.

Alternator/regulator problems should get it taken care of quickly as failing alternator/regulator can spike the voltage overcharging your battery, you could lose that also.

__________________
X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas