Yes, climate change is very possible. I made a similar move, from California to DC, and the humidity here causes a lot of allergy problems. But you know, sometimes a run causes this if you're tired or it's hot or it's just not the best day or you're in a new climate and altitude, it doesn't mean it will happen again or you have to medicate yourself. You just have to get used to the new environment, most likely. By the way, don't know what you mean by a paleo diet, given we don't really know what people ate before recorded history, we just have theories and some historical finds. The right diet is the one that you digest best and gives you the nutrients you need, and that isn't the same for everyone, and it might differ depending on climate as well.
Paxiled gave you some good comments. Switching to a new climate will sock it to you sometimes. If you have tender lymph nodes, that could be an indicator of allergy symptoms or inflammation. Drinking water is good, but your symptoms could also mean your electrolytes might be out of whack. You might consider trying a 1/2 and 1/2 combo of gatorade and water, or adding juice or other liquid nutrient to perk up your levels a bit.
Allergy meds will definitely make you sleepy. And, any move can be stressful. I'm not all that familiar with the paleo diet either, but I would say if the symptoms persist for another week, I'd follow up with a regular doctor. In the mean time, rest, be kind to your body, and give yourself some time to adjust.