
I'd hazard a guess and say that you had a "UV/whatever" filter on your lens, and that this is a reflection of the bright area on the left. You can see from the line that I've drawn that it's directly opposite across the centre of the lens.
This is one of those times you definitely DON'T want a filter on your lens (or want to have spent lots of $$ on a filter that's well coated to try to reduce the likelihood of this happening).
As for the 2nd image, that IS flare that you can see. A hood will protect against bright lights coming from the side, but here the flare is being caused by the bright areas within your field of view. Again, your UV filter is partly to blame here!
Exposure/processing decisions (as per Gary's comments) can help here (e.g. increasing the Blacks slider in ACR can help hide it) but the underlying problem is a physical one on the front of your lens.
Shooting with a hood is great: keep it up. Not only because it will help your images, but also because it will help protect the front of your lens when you're shooting without that filter.