You cannot use the present perfect when the time phrase in the clause excludes the present.
In your case, on a semantic level, speaking from a point in time where you are no longer in primary school, but in high school or university, the phrase in primary school refers to your past, excluding the present.
But if a student in primary school wins a Nobel Prize for inventing a new kind of chalk that erases itself:
I have won the Nobel Prize, and I have won it in primary school.
In this particular speaker's context, in primary school does not exclude the present, and the sentence is grammatical.