Teething + Sneezing/Runny nose? Related?

DD is cutting her bottom molars.  She woke up this morning with a really snotty nose this morning out of the clear blue.  This is day 2 of her noticeably teething (drool, chewing on everything, hands in mouth, etc).  She's also sneezing.  There is no color to her snot.  She took an extra long nap today.  I went up to get her and found her laying awake in a puddle of vomit.  No fever and didn't even move when she saw me.  Didn't flinch.  Scared me to death.  

 I got her up and put her in the tub and she's seemed totally fine ever since like nothing ever happened.  I heard her cough one time on the monitor (but she hasn't been coughing....so it was random) and I think that's when she may have thrown up...possibly from the mucous in her throat?

 Like I said...she's running around playing and seems just fine and I know for a fact she is teething.  What does this sound like to you? Contagious or no?  I don't want to have her around other kids if she's sick.