Goining crazy, could use some advice

So here is my story.
I am separated and was not looking for anything, especially not when I went to the hospital for a minor procedure just before Christmas.
So, I am lying there in my bed and am actually in significant pain when one of the nurses comes in. Of course, I can only see her eyes since hospital employees are to keep their masks on at all times when with patients.
But non the less she walks in and just mediately lights up the room. She talks a bit to me as well as the other patient in the room and I am just in awe of her kind way.
So the next day, I have had my procedure, and am feeling much better, sleeping a little as I am woken up by her, just stroking my hand and apologizing for having to wake me up to change my infusion, especially since I looked so cute sleeping.
And I am struck again thinking, that she is just a creature beyond lovely. So, at the end of her shift, she comes into the room again, stands at the end of my bed, and takes off her mask for a moment just to tell me that she will be back tomorrow night.
At this point I get the first inkling of a holy crap could this be happening. Anyhow it is the night before I am to be released at about 1 am and I feel fine but restless, so I take a little walk. She is the only nurse on night duty at the station and she comes out of the nurses' room as she notices me walk by. We talk a little and she tells me that there is rarely much to do at night so after 3 she usually just sits in the kitchen next door and if I still couldn't sleep she would not mind the company.
So, at 3 am (I am fairly tired but who would care) I take her up on the offer we establish a first name basis (which is apparently against hospital policy) and we just sit there and talk till about 6:20 am. As she casually mentions how she had been unhappy with her last boyfriend only to quickly add that he was history now.
Unfortunately, at that point here colleagues from the next shift arrive and the situation becomes a little awkward as I was technically not supposed to be in the room. And so, I politely say my goodbyes with her just adding not to forget to come by when I will be in for my follow up 2 weeks later.
After I came home and slept for about 12h I just found myself completely incapable of thinking of anything else. So, wanting to kick myself in the bud for not asking for her number, the next day I write a letter thanking her for her company and the conversation that has been stuck in my head, expressing my regret about not getting her information and leaving her my number. I hand the letter to the hospital clerk who promises to see to its delivery. Unfortunately, I have no idea when she will be on duty again and if my message will actually reach her.
Now it has been 70h and I am finding myself sitting on a box containing the worst Schrodinger’s cat of all time, wondering if I might misread the situation that badly.