Did you check to see that you pulled the gasket out with both of the old bulbs? Try pulling them, check all is in order, and reinstall.
If one of the old gaskets stuck on the headlight or it is not inserted correctly it can change the position of the bulb enough to throw off the high/low beam angle.

 

I did check for gaskets. I changed a lamp last year and when I couldn't get the new lamp inserted I discovered the leftover gasket stuck up in there. So I was aware this time.
I just checked the lights as it's getting darker and everything seems to be OK. Still a funny pattern on the door, but high's and low's do seem to switch on and off properly. It looks like the low's stay on and the high's are added to that.

I just discovered that small black piece is made of rubber not plastic as I stated above.

 

It looks vaguely like the ambient temp sensor; does the ambient temp work?

 

It is not the temp sensor. I found this pic at Napa: https://www.napaonline.com/en/p/ECHTS5038
I can take it to the dealer parts guy and see if they can Identilfy it.

I used the car last night and the lights are OK, but still a odd pattern shining on the road. No one "blinked" at me and I could see fine. Maybe as mentioned before - the lamp was not made right.

 

The stock sensor on 2010-2011 is different. It sort of hangs under the radiator on the driver side, maybe clipped to the bumper cover.

 

Eddie's profile says 2009

Eddie, you say the part fell from the right side, which is passenger side. Just so we're all on the same page.

 

Could be a part from his car. Also could just be road debris that got wedged in there and fell out when changing the headlight bulb.
(just trying to think "outside the box" so to speak)

 

Yes, is was on the passenger side. At first I thought it may be a "breather" tube for the headlight shell. When you look in that square hole there is a white colored membrane with a jagged hole in the middle of it. I'll take some more pics of it.
It may not even be from this car as stated !!! Maybe I've been carrying it around for some time - and just knocked it down from it's hiding place. Sorry for the size. I don't know how to change them.

 

Could be a vent cover, I’ll check I’ve got an extra set of headlights

 

I was going to say the same thing looks like a vent cover to me.