Christoph D. answered 05/20/19
TOEFL Prep Tutor Experienced in Helping Students Achieve Target Scores
In this situation, I would reach out to the admissions department directly to explain the situation to them and ask them if they'd like you to send them an electronic image of your unofficial scores. One way to approach it would be to first simply ask them whether they've received the official score report yet. Then, assuming they say no, you could respond by assuring them that it should arrive any day and that in the meantime you would be happy to send your unofficial report to them if they require it immediately.
And unfortunately, no, I don't believe ETS sends out any sort of notification to let you know when official score reports have arrived. You would have to look at your application status online through the university's website and/or contact the admissions department directly.