You're scared that one day she might actually need care?  I think that if she needed a trip to the ER you'd know. You don't go to the ER for a sore wrist. I'd say it's time someone told her the story of the boy who cried wolf ...

If your husband and you have separate finances, the cost of that trip should come out of his own money even if it's from hissavings. It does NOT come out of the household account. That might teach him to be less gullible in the future.

What exactly did she claim was wrong with her? 

Don't get upset to an extent that your SO is aware, it will affect your relationship. Find your own corner and get it all out of your system, so you can be relieved of the emotions. This is also the perfect plartform to let it all out, I also find gym/exercising and sleep helpful. I would be very angry everytime SS did something and it would ruin my weekends. I now realise that getting angry is only affecting me and ruining my weekends. SS would continue with SO like nothing happened, SO would just brush it off like it's nothing and I would be more mad at not only SS, but also SO. That's when I realised that some BFs will never see anything wrong with their bio kids' undesirable behaviours, they look the other way and expect all of us to accept. 

I suggest you try to find a way to deal with it everytime it happens, cause I can promise you for as long as your SO doesn't see anything wrong with it, SD will continue, 'cause she has seen that it works to get the attention she requires from daddy, you and your SO will cotinue being at loggerheads because of her. I say accept what you can't change, because voicing it out makes you seem like you are heartless for not understanding that SD needed medical attention, even though deep down you know she is faking it. It's not worth you fighting with your SO, you will be playing right into SD's tricks, that is what she is hoping for...tension between you two. It's ok to be angry, you have every right to be, just go through the emotions, get it all out of your system and pull yourself together, not showing that SD's tricks get to you. She will eventually give up her nonsense if she realises it does not give her the intended results. If she sees the effects on you, she will press hard to frustrate you. If I were you, I'd let SO pay for the medical bills alone and not even assist, so he can also feel the impact of his kid's tricks. Hoping that one day, he will see through her and stop her. Sometimes I think some of these SKs are influenced by the BMs to frustrate the SMs. The trick is to not give them the satifaction of seeing you affected by their nonsense. I'm not saying pretend, but find a way to deal with the emotions that come and be ok. There isn't much you can do for as long as your SO is still siding with his kid and doesn't see anything wrong with her actions. 

Good luck!

SD is controlling your life.  You have a right to be upset .SD is trying to gerbyou and DH fighting over this. "Controlling the hone". 
The question is how do you react. How do you take back control.   Plan a really fun expense thing to do.  Next time SD goes to ER ,,  you go to X have a good time.  Send text I at having lunch.  Picture included.

There was some serious stuff going on - can you fill us in?

Oh hell no. Next time, tell daddy to call an Uber because you are not ending your day for the fake illness manipulative spawn.  Order a cool umbrella drink and call to book spa appointments while he is booking his Uber.