My suggestion for wording would be to change 'mom' to 'mother' as this is a formal letter, and 'mom' sounds a bit informal and doesn't quite match the tone of the rest of it. In the first part, your mother 'had already spoken..." Be sure to capitalize 'May 3rd' and also the full name 'Michigan State University'. "The reason why I missed the AED was a misunderstanding" sounds off, and could maybe work better as "I had missed the AED due to a misunderstanding."
Also watch your run-on sentences. Your entire letter is only six sentences. In your last three lines, make the parts beginning with 'I spoke to...' and 'I'm sorry.." their own sentences. You might also consider rewording or striking completely your second 'upcoming fall'. It sounds slightly superfluous having two of them in one sentence. In the second part, 'after telling him my situation, ..." should be its own sentence. In the first part, put a period after 'misunderstanding' and start the rest as a new sentence.
Just my thoughts, hope it helps
(not a teacher, just a language lover)
Student or Learner