Alabama does not have a CCW permit. It's a 'pistol permit'.
If the permit is qualified, and prohibits carrying into a 'public building', than I would ask the Sheriff to clarify. It wouldn't include Wal-Mart though.
Whatever location restrictions were on your pistol permit would not apply to OC, however, as the permit only pertains to CC.
Anyways, the location restrictions are something you need to ask your Sheriff about, because he is the one who sets them for each permit.
Otherwise, Alabama has essentially zero prohibited places. Check Code of Alabama 13A-11-50 and up. The only prohibited place by statue is a public gathering, but it's very narrowly defined, and not what someone would generally consider a public gathering.
Also remember that Alabama has full preemption for handgun laws. No locality can make any rules, ordinances, etc, that are stronger than state law, even on discharge (and state law is virtually nonexistent). If you work for the city they can't even prevent you from carrying on the job.