It has been a week should I call HR?

My interview for my dream job was one week ago. The hiring manager/head nurse basically offered me the job "informally" on the spot. We really clicked and she told me I have the job. She even walked me to HR to sign some papers to get the ball rolling. I have not heard from HR. The nurse manager did email me and said she would "be in touch" with me. What should I do? Should I call HR and check the status? I know HR is short-staffed, but my orientation starts in 3 weeks and I'm not going to resign until I get a formal offer.
A couple of thoughts...1) I'd be more likely contact the NM who hired you. You might get blown off at HR, the NM won't. I'd just reply to her "in touch" e-mail and ask for a general timeline.2) "I'm not going to resign until I get a formal offer." - Offers can be rescinded, you know. I just want you to realize that you're not out of the woods until you're on the payroll.