The first thing is, where are your elbow rests on your tribars. Generally you should be in a position that allows your shoulders to be at a 90 degree angle to your torso. In a aero position you want your back to be flat. The aero position does put more pressure on the soft tissues/girly bits, because you pelvis is rotated forward. For this reason, it's generally a more uncomfortable position unless you're cranking it. When you're applying more pressure through the pedals, it takes pressure off the soft bits. If you are rotating your pelvis back bay sucking in your belly, you will take the pressure off the front (this is why most people do this, to relieve discomfort, often subconsciously), your back and neck can get more sore.
So what should you do. You might need a flatter saddle (saddle shape, not tilt) to keep you from sliding forwards in the aero position and you may need to actually move your elbow pads back if possible.
What I've learned over the last few weeks of trying to decide what bike to buy is that it is really hard to achieve a efficient aero position on a road bike. The 2 suggestions I made may help.
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2007 Look Dura Ace
2010 Custom Tonic cross with discs, SRAM
2012 Moots YBB 2 x 10 Shimano XTR
2014 Soma B-Side SS