Is this sentence OK?

"May allowed" should be corrected to "may allow".

After that correction, the sentence should be "technically" correct, but the style is very awkward/passive. The focus of the sentence is currently on the word "email." Are you really trying to focus on "you" and the opportunity to become a second year student? If so, then a better revision of this sentence would be:

I received a surprise e-mail asking me to do a test to become a second-year student.

Just my suggestion as an English teacher/editor.

The 'allowed', as the above said, should be 'allow'. And I think it might not be 'became' surprised; rather:I was really surprised.