Oh no you are not harming her. Actually doctors say the best side to lay on during pregnancy is your left. It is also very normal for your baby to have hiccups while you are pregnant. They are preparing there lungs and the hiccups are harmless. My baby girl I am pregnant with, she hiccups when I am sitting up right. She hiccups whenever and it actually makes me feel alot better to know that she is alive in my belly besides all of her movement and rolling.
My doctor told me that hiccups are always good. The baby is practicing breathing. Not sure why you only feel them when you are on one side but that is probably just how the baby is laying. I always felt them on my right side with my daughter and left with my son.