I wonder if it is a food or ingredient in the new foods you added? Seems quite possible.
If they are taking out wheat and dairy, they are replacing them with something else. I would read the ingredients very carefully. See if there is a grain or ingredient or additive you are not used to, and are having a sensitivity to.
I'd try that before adding back wheat. You could even skip ALL the new or unusual foods for a week or two, including the cherry coke. Just eat whatever you were eating before, minus the wheat and dairy. If your lips clear up, you will know it was a reaction to some food or ingredient you recently added. Then you just have to figure out which one.
Also, when you started drinking more soda, did you drink less water? Soda is actually rather dehydrating, and if you were not drinking plenty of water in addition to the soda, your lips might have gotten worse from plain old dehydration?