Don't just go in to urgent care - waste of time and money until you have advice to do so. I'd call the pediatrician's 24/7 line and describe the rash, ask what to put on it (if anything). You can ask what's safe for the stuffiness too.
Rubbing her eyes can mean there's some allergy stuff going on (which can contribute to the stuffiness/sneezing and even the rash), or it can be the start of conjunctivitis which happens a lot when someone has a cold. I know it's impossible to stop a child from rubbing the eyes after the hands have touched the nose, but do try. Lots of hand washing but please, not with antibacterial soaps, just regular hand soap and rubbing and lather. If the eyes get worse and if she wakes up with a crusty discharge, wear gloves and use a warm compress to soften them, and then DO go in to get antibiotics because it's highly contagious and you definitely don't need the whole household to have pink eye!
Try elevating her head at night - fold a blanket or some beach towels and put them under the mattress at one end so the whole mattress is at an angle - easier than just trying to prop her up on pillows, which she will roll off of at night.