Throwing up is not usually normal for beardies. I did have both of our girls throw up, once. For Rosie it was because her temps weren't correct and we had just gotten her a day or two before. With Goldie, she ate too many supers too fast without chewing them first. But neither of them got diareha, though.
What are your temps? and what do you take them with? That may be part of the problem, tho with the two, I can't be sure. Is there a vet near you that specializes in beardies? Where we are there isn't and we have to go to Tucson, AZ to see one.