I think you should definitely get a second opinion. For the truly adventurous, a biopsy is the way to determine if you have actinic cheilitis, but from the looks of it, it doesn't seem like it. It's very interesting that your peeling would be asymmetrical after all this time, and that the condition went into remission in hot climates. Were they humid climates as well? Did you change much about your lifestyle there, your hygience, your diet, your general mood?
I've been using a stronger steroid than Triamcinolone lately and there may be an increase in my stress, but I'm doing everything I can to limit it. I may switch down to a milder steroid now that it's been a month and there is still some peeling. Keep us posted on developments with your condition.