Is it possible that my partner did not got chlamydia and i did?

Unlikely: If you have it he most likely has it also. He just does not have symptoms. If he is not treated when you are, you will very likely get it again.

Very unlikely: If you caught it from someone else, your partner might not yet have caught it from you. However, it's more likely that he also is (or was) infected. The tests aren't perfect and miss some infections. Also, infection usually clears up over a few weeks or months, even without treatment -- so he might have had chlamydia but now gone. Your partner must be treated, even though his test is negative.