You 上 a school. The school's name is often transliterated.
上小學 - To attend primary school
上中學 - To attend middle school
上高中 - To attend high school
上大學 = To attend university.
If you are a university student, you can say something like
我在劍橋大學讀書 - I study at Cambridge University
我在曼徹斯特大學念書 - I study at Manchester University
我在倫敦學習中文 - I study Chinese at The University of London
You use 年級 to say what year you are in.
我是大學一年一的學生 - I'm a first year student (freshman)
This can be simplified to 我是大 - I'm a first year
Generally, a self introduction 自我介紹 is written like this: