Hello Jenny: My condolences on your daughter's loss.

In answer to your question, at least from my perspective, yes... how you're feeling is pretty normal. There have been a couple of people I've known over the internet who have died. I never met them & really didn't even know that much about them. But I still felt badly leaning they had passed.
In your case, you had come to know your daughter's bf even though the two of you had not met. And, in addition, I'm quite certain you have great concern for your daughter's welfare. As you wrote, you feel horrible for her. Some counseling for your daughter will probably be most helpful for her. It may also help you just to know she is being cared for. However, if you find that your own grief & anxiety is not subsiding, you may want to consider seeking some counseling or therapy for yourself if you are not presently receiving these services. Continuing to post here on PC may be helpful as well.

My best wishes to you both...