Is there more caffeine with an AeroPress? I like everything about the AeroPress; however, I noticed that I exhibited symptoms which I usually only have when I've consumed too much caffeine. 

So instead of using two scoops during preparation per instructions, I scaled down to one. That seemed to help, but not enough--if I use the same coffee and amount in a conventional coffeemaker and consume it all in one sitting, I don't feel over-stimulated. 

Does the AeroPress simply make "stronger" coffee with regards to caffeine content?
Aeropress coffee (hearby called Aerpresso in this post) is more concentrated than regular drip coffee.  However, if you are using similar amounts of grounds as you would in a drip machine, you shouldn't notice any difference.  Caffeine is highly soluble in hot water and most any extraction method utilizing hot water will result in nearly full extraction of caffeine from grounds.

Aerpresso ends up somewhere in caffeine concentration between espresso (very concentrated) and drip coffee (less concentrated).  However, the total amount of caffeine is dependent more on the amount of grounds used that the extraction method (with the above listed methods). 

So the the final answer is no.  There isn't more caffeine, but the Aerpresso is more concentrated.