Rebekah, it does seem such a shame. Like you say anyone can buy those hearts & put them on a cozy. Hearts are so popular it's bound to happen. I don't know why they thought you were copying then, maybe it's sheer chance they look alike. Wait for Etsy to reply to you. It might get sorted out.
Your cosies are lovely. I sell some too, they're sweet to make aren't they? 😊
There must be tons of things that look alike; jewellery, knits, belts, polymer clay food! The list is endless. I don't understand how one person owns rights to it but hope Etsy can come through for you .
Good luck flower!