Well, I can tell you that you tested too early. Even if you are pregnant, it would not be positive yet. Generally HPT's don't turn positive in pregnant women until 10-14 days after ovulation occurs. So if you have 28 day cycles, which by the dates you have given it looks as though you do, then you would have ovulated on December 12th. You BDed on this day as well as several days before this, and sperm can live inside your body for up to 5 days if conditions are right.
I am not familiar at all with the Nuva ring, but putting that aside, it is definately possible for you to be pregnant given the days you had unprotected sex... especially since you started the birth control mid cycle. On the flip side, it is also possible that the symptoms you are feeling are from the effects of the birth control, and perhaps the fact that you started it mid-cycle is throwing your body a little out of whack.
But I would definately say you sound like a pregnant lady

You should wait until around the day your period is due (14 days past ovulation) to test again and you will get your answer then!
I am not sure if you are hoping to be pregnant or not but I hope you get the answer you want!
Good luck!