Question about hiring process/background checks

I was offered my first position at a hospital pending my background clearance. They also asked for a copy of my highschool diploma. I was homeschooled throughout school and do not have one, but I did complete a GED. However, when I contacted my highschool today they told me my GED cannot be issued until I complete the one more portion of the test. I thought I had completed it at the time. I never contacted the school after taking the test because I have never needed proof of my GED until now. My university never asked for it because they accepted homeschooling as evidence of my completion of high school.
I have made arrangements to complete the one final portion of the GED this week and they said the certificate could be issued within two weeks.

I am really stressing out about this!! Should I just email HR and tell them that there is a delay in my certificate and it will be complete in 2 weeks? I was honest with HR and they do know that I was homeschooled and took the GED test. I told them I was not sure about my certificate. I hope I don't lose the job offer over something this silly!!