My daughter swallowed a coin, her airways seem open and clear and she says she doesnt feel it in her throat any more?

If it's anything except a quarter, in a 4 year old, this will pass. Quarters are a bit different- in her age they can get stuck at various places down the esophagus, so bbn if over next few days she has any complaints of pain, not wanting to eat, difficulty eating, then she should have an xray to determine where that quarter is. If padt her stomach, then it too will pass.