请看这段英文翻译有没有语法错误，中文意思如下。

I am excited to receive your conditional offer of admission. I note that as indicated in the offer, I am required to provide the test results as proof of my language skills by June 1, 2015. I am writing this letter to request for a late submission of the test result, as I have just taken another test and the result will be issued until the end of June.
XXX University is my dream school and my only choice for post-secondary education. As I have not submitted my application to other colleges. Therefore, I really cherish this opportunity to be admitted to XXX University.
Hopefully my request for a late submission of the required document can be granted.
Yours faithfully,

译者寄语：
写这一类的请求信，应采用标准的公函格式。故此，应先表明你的要求和理由。须知你的个人对大学的热忱不是充份的理由。假若你有别的理由，请自行修改。

I am very excited to receive my conditional offer. Your university is my dream school, and you are the only one to which I submitted my application. I really appreciate you give me this opportunity, but I have little worry about that I did not submit my language scores before the deadine time(1st of June). I wonder whether it is acceptable to submit in late June?
英文逗号和句号很重要，一句话结束一定要标句号；另外使用从句要注意代名词使用方式。

楼上的改的不错，你自己把意思都写反了，I have little worry about which这个地方，你这意思是你不怎么担心。。

It is my pleasure to receive the conditional offer, XXX university is my top and only choice (I have only applied XXX university), so I would cherish this precious opportunity, However, I have a little concern about handing in the language score on time (as I have see the requirement saying handing it by 1st of June), so I would like to ask is it possible for me to submit the score later (like later in June)?
Thank you!

有些地方不好，改了一下。

I am excited to receive your conditional offer.And I see one of the requirements for admission is to submit language scores before 1st,June.XXX（学校名） University is my dream school and you are the only one to which I submitted my application, so I am really appreciated and will cherish this opportunity,but what I am worrying is that I may not be able to submit language scores in time due to some reasons.So I wonder whether it is possible to submit it later,like in late June?