Chances are that it's just her being a newborn. Their little nasal passages are really wee, and they are still expressing mucous from being inutero, plus dealing with dust and other irritants. Most babies are noisy sleepers and breathers! Do you have a nasal aspiriator?
If you are really concerned or if she isn't eating well, then take her to the doctor or emerg, but it is completely normal to have a snarfy baby!
It's also completely normal to fear they'll stop breathing if you take your eyes off them. :) It will really benefit you both if you get some sleep though, even if you let her sleep in a swing/crib/pack n play etc. right next to you.
I'd discontinue the Vicks for now, the saline drops can be useful especially with an aspirator, and a cool mist humidifier can help if she really has a cold but just know that so, so many babies get snuffly. Especially if they were C-section babies. However, both mine were born vaginally, and both were plenty snarfy.
Editied to add - if you are breastfeeding, she likely will have gained some immunity to the cold through your breastmilk. It's really uncommon for a 3 week old to have a cold, so honestly, if it seems really bad and she can't eat and is struggling to breath (again, most babies are normally noisy sleepers), if she is wheezing, etc. I'd take her in immediately. :)