Should we take her to the hospital?

My husband was holding our two year old and she was mad, she flipped back and he caught her by her arm, otherwise she would have hit her head on cement. She starting crying holding her wrist, it doesn’t look red, swollen, or out of place. We assumed that it just hurt and she would be okay. It’s been about 30 minutes, she’s in the bath and she’s not crying anymore, seems very happy. She’s using her hand, but not much. She’ll move it, then stop and cradle it. But doesn’t cry. I’m not sure if we should take the hour trip to the ER or not. My husband is worried they will call cps and try to get her taken away because when I was 6 I broke my arm and they arrested my dad when I literally just fell at the playground. 🤦🏼‍♀️ but of course we will take her if need be. Does anyone know the signs of a sprained wrist in a toddler? Maybe it’s just sore? Please help 😩😩

The reason I ask is because we will have to take a taxi over an hour away to the hospital because our car is getting fixed and won’t be done until tomorrow so I don’t want to do all that if it’s nothing

Update: everyone being rude saying cps needs to be called because we are worried about it. 🤦🏼‍♀️ did I say we weren’t taking her because of that? NO. I said we didn’t want to make a trip an hour away if I’m just over thinking it and she doesn’t need medical attention. There are no Uber’s or lyfts in this area and most taxi places will not come out and drive in this weather so our only option would be to call an ambulance for her OR wait until another day. Thanks for the nice comments, we put ice on it. I can move it and touch and there’s no reaction. She’s just babying it but I seen her put weight on it a few times so we are going to give her some medicine and see how she is in the morning. For all the negative comments, please review yourselves. Thanks 🤦🏼‍♀️🤷‍♀️😊