Anything you might try using to pull it out could cause injury and make things worse. I'm not sure if the stuff would break down on its own or not. Alginate does shrink when it dries, but it's not likely to dry where it's at. Much would depend on just how much is involved and far in it went. You probably should get professional help with having it removed.
Considering what happened you must be doing something wrong. The area around the nose s/b the last thing you dojust before removing the mold. After the plaster is in place you brush a little baking soda - water solution on the cured alginate and then carefully add new to area around the nostrils being careful not to cover them completely. You can also do the straw thing but it has its drawbacks.
You really should try contacting someone close to you that already does lifecasting and ask them if they'd show you the proper way to do this. There's a list of lifecasters with addresses and e-mails on the ALI site:
http://www.lifecasting.org click on Directory. There's 19 pages of names there.