My dog has a foxtail in her nose what will happen if we don't get it removed:( :(

I am assuming you are speaking of the grass foxtail. You need to make an appointment with your vet. The foxtail needs to be removed. If left untreated, it can lead to infection. I don't want to alarm you but in some cases, if it is severe enough, it can lead to death. Please read the info provided on these links:

Dog Owners' Guide to California Foxtails

Foxtail (diaspore) - Wikipedia, the free encyclopedia

Is it dug into the skin or just stuck up there?

If Ruby's post didn't convince you, check this: Ecclectica - Foxtail barley: a threat to your dog I disdain sites Googled up at random. This came from the Woodhaven Labs site which I have known for years and mostly found trustworthy, unlike much of what is on the net.

I have never had a dog get a foxtail in its nose and didn't realize how serious it is.

Excellent resource site labman! I generally don't like Wiki but couldn't find anything else to give additional info on this. I felt the other site, even though it was from an educational source, didn't have enough on it to create the concern I was trying to get across. I know of one person whose dog had some severe problems caused by foxtail embedding itself in his ear.