That definitely sounds like the medium was too tight. I have relatively large arms, chest, and neck and don't have any discomfort or breathing impairment (I wear the men's XL). I'm hoping the large works out for you. I don't think you are supposed to wear anything under it, even a bra...but what would I know in this regard? My wife wears multiple different women's sizes depending on the brand and the garment. I've learned to always by the smaller of the sizes and let her exchange if she needs to rather than insult her.

I had the unpleasant experience of having to take the IntelliSkin on and off while having an IV in my arm in the ER. With my wife's help I was able to very carefully get it on and off one arm at a time only having to raise one arm over my head. It may take a little practice but the stretchiness of the shirt helps you to maneuver it on if its the right size.