Running out of time!!!

Good morning, my fellow nurses! So last week I verbally accepted a job offer with Northwell (formerly North Shore LIJ) over the phone but they haven't emailed me my offer letter yet. I need to give 4 weeks notice to my current job in order to have my vacation hours paid out and the 4 weeks notice needs to be given TOMORROW. I was told by the lady that the offer letter that would be emailed to me has a link that I click to confirm that I am officially accepting the job which means I would be safe to hand in my resignation letter. By the way, is this something new? I always thought you have to physically sign the offer letter? Upon accepting the job verbally, I told the lady that I need to give 4 weeks notice so if she could send my offer letter sooner that would be great and she said she would. I called her this past Tuesday just to remind her again and that I needed to hand in my resignation on Friday (tomorrow) in order for me to give my 4 weeks. She said she'll put my offer letter at the top of her list to work on. She was very nice about it and I apologized for making her feel like she had to hurry my offer letter.

What should I do? I feel so anxious right now!

1. Not call the lady since I called her on Tuesday already, HOPE she sends the offer letter by end of this week, hand in my resignation tomorrow and hope for the best?

2. Call lady again today in the late afternoon to remind her again? I feel bad bothering her especially after she's aware I need it soon but I feel uncomfortable handing in resignation with just accepting a job offer verbally.

3. Not call the lady, wait until she sends me the offer letter, then hand in my resignation letter and lose vacation hours (I don't know how many I would lose)?

4. Any other suggestions?

TIA!