Hi Myeung
You can say these, for example:
- I
was born on January 22, 1990.
- My brother
was born in 1988.
- You
were born a year earlier than I was.
- My brothers
were born on the same day -- they're twins.
Do you remember any of the specific sentences in which you saw "I were born"? Generally speaking, the only time you will see "I were" is in a conditional sentence, or perhaps an "I wish" sentence.