First, regarding the structure of your letter:
+ In the first paragraph, you should state briefly the purpose of this letter, for example: "I am writing this letter to request a review of a recent decision...".
+ The second para is where you tell the story. Don't tell the whole story in the first paraghraph and then say "This is why I am here writing an appeal".
+ Third para should be why your appeal should be granted (which is your current second paragraph).
+ At the end of the letter you should have a closing sentence like "I appreciate your considering my request..."
Secondly, make sure your grammar is correct and check your wording:
I decided to follow up on this and called themadmissions office .
--> "follow up on" is not formal, it sounds like you are talking to your friend. Replace "follow up on" with words like "verify" or "inquire into". And I don't get what "this" refer to.
two months later
my application was received late on file and that it willwould not be reviewed.
I would hate to lose out on more time
--> this is not formal.
And don't use contraction like this:
I really hope you'll reconsider
Lastly, watch your tone in the letter. Keep a respectful tone.
I explained to him my situation but all he could say was sorry, what you could do is go on the school's website and ask to defer my admission for the spring semester.
--> Leave out this sentence, the admissions office does not need to know what the counselor told you.
Hope this helps. Good luck with your college admission.