TUMMY SLEEPING QTNA

My daughter has acid reflux pretty bad and has been taking medicine for it going on 2 weeks. To help her with it we swaddled her and put her to sleep in her rock and play. (Her first week home we laid her to sleep on her back as directed and she spit up out her nose and mouth and wasn’t breathing...so scary!☹️) but now she has been napping SUPERVISED on a crib mattress face down with a fitted sheet.

She lifts her head and turns it side to side and when she does go face down it doesn’t bother her because it’s such a flat surface and she always turns her head back over.

Dr says sleeping in rock n play for long period of time can cause spinal issues down the road but I’m TERRIFIED of her chocking on her spit up again should it happen and we are asleep in the next room. I was told I’m not supposed to lay her on her stomach because of SIDS but my back is against the wall...

Advice?