No, you're not going crazy. (Well, that's a broad statement, let's just say on this case you're still sane). Some of the more eagle-eyed of readers might have noticed I've gone back-in-time and replaced all of the "Al Aqah"s with "Al Aqqa"s when talking about our trip last weekend.
Both are right. When I got home and was writing about our trip I googled it, and "Al Aqah" came up first. But then later I remembered the road signs to and from the area spelled it "Al Aqqa". And I think that one looks neater.
That happens quite a bit here, words or towns have multiple spellings. On old maps Dubai is sometimes spelled "Dubayy", even. I guess this is because the name is not being translated into English, it's only being transcribed from a different alphabet (from the Arabic alphabet to the Latin alphabet). So "Al Aqah" sounds like "Al Aqqa", and "Dubai sounds like "Dubayy".