Is this sentence tense appropriate?

The tense you are using had shut down (past perfect) does not sound natural in the context of your sentence. Think about it in terms of a timeline. Consider that there are two events:

Event A: the professor wrote something
Event B: my brain shut down

The past perfect is usually used in the clause talking about something earlier, rather than later. By using the Past Perfect, you are telling us that B happened first, and then A happened. So if "my brain shut down" happened first, what is the connection to the professor? The intended meaning is not quite clear. Here is an example of how to use it to clarify the sequence of events:

My brain had already shut down by the time the professor even started his lecture.

In this case, the Past Perfect is appropriate because Event A (my brain shut down) happened before Event B (the professor started his lecture), and implies that you were not mentally prepared for the difficult lecture.

If you want to say that Event A and Event B happened at exactly the same time (no cause and effect), then you still should not use the Past Perfect since it establishes a relative timeline. You could change it to something like this:

Just as the professor wrote on the board, my brain shut down.

On a side note, your use of 'officially' is quite interesting. It sounds a little unnatural to me but it's difficult to explain why. I think it might be that 'officially' is often used as a kind of emphatic way to present a logical conclusion, after you have listed some reasons. Consider this article, titled "I am Officially Sick of COVID-19". The writer talks about many different reasons which caused this non-literal 'officially' feeling. Maybe the reason your use sounds wrong to me is that there are no causes presented beforehand. You might need to explain a few causes when claiming the final conclusion of 'officially ...".