Hard to breathe during meditation

I started with a new goal: meditate for a month daily and it reminds me of my experiences during group meditations in the past. After relaxing the body, it gets very hard to breathe, my chest feels very heavy or like something is on top with a lot of pressure. I feel like I should breath deeply all the time, yet still feel like I don't have enough air. A bit scary too. Has anybody experienced the same?