Choking ...

My 4 week old preemie (36 weeks gestation) seems to have a little reflux. Her pediatrician is hesitant to put her on anything because she says she doesn't seem too bothered by it. Even though I told her that she has a random cough (not a "cold cough" but more like a "tickle cough") and chokes when I burp her sometimes. She is also really figidity sometimes.
Both my boys had reflux -- my oldest had a horrible time (and he was 10 days over due).
Anyway .. The dr said the choking really isn't a sign of reflux. But she burps, I can hear that it's a wet burp and then she chokes. She chokes because the milk comes up, she aspirates and chokes.
Anyone else have similar stories?