And on top of the other poster's information given I would also highly advise against feeding your Beardie something like that in the future.
For the reasons like that given, it's just not a good idea as it could cause things like that. But also it could be a choking hazard, it could cause an impaction, it could give them parasites, and many other things that just aren't good. Feeding your Beardie things like other lizards or pinkies are a bit of a controversial topic but to be on the safe side I wouldn't recommend it. Pinkies I'd only be ok with if it was a VERY small pinkie and the dragon was rather large but maybe a bit underweight or something. But other lizards? Ehhh... I'd just steer clear from that. :|
But please get your Beardie checked out by an experienced reptile veterinarian to see if the skink caused any problems. Did the Beardie just find the skink outside and try to eat it or did you purposely feed him it? Did she actually eat it all or did the skink get out and is it still alive?
To help your Beardie with recovering I would recommend getting her rehydrated, Put a small pinch of calcium in with the water you're giving her and that should help, but really try to rehydrate her, maybe give her some more electrolytes, and just more TLC and a vet visit. And no good until an all clear by a vet too. There's a very good chance she will bounce back from this rather quickly.