What to do when a tick head stays stuck under the skin?

So i have a little West Highland White Terrier puppy who has a tick on her snout. I took it off with a pair of tweezers, but i think the head is still inside. The area around where the tick was is swollen and it looks like a little part of it might be inside. I don't know if I can go to the vet until next week but I know someone who's cat died after two days because of this (I don't know if that's really true or not, but I don't want to take chances). What can I do about it? I know some people say that the skin will eventually push it out, but others say to take your dog to the vet immediately. Help??