writing

This should be made into several sentences.  You switch back and forth between present and past tense.  The passage should be one or the other.  Are your parents still in the USA?  “Were” is past tense, which indicates that they are no longer there. 

Fellow is an unnecessary word, as it carries the same meaning as the mate part of classmates (which is one word).

When your classmates assume that your grandmother is your mother, does it always make you cry?  We usually use either begin to cry or cry a lot, but not both.  Perhaps you just need the reader to know that it makes you sad, rather than sharing about the amount of crying. 

It is not easy to know what your classmates don’t understand.  Do they not understand why you are with your grandmother, or do they not understand why you cry?

“Anyhow” is an informal and conversational word used to jump from one thought to another.  It is usually used when one is getting off track or rambling.  Your usage actually is how you might hear some native speakers talk, but it is not grammatically correct. 

I get sad and cry when my classmates assume my grandmother is my mother.  Even when I explain, they don’t understand.  I am proud that my parents are in America.  I dream that one day I will be able to go live with them there.

I hope I didn’t change your meaning.