A balanced diet and plenty of water are important factors in preventing calcium crystals. Is the raw diet that the vet mentioned you are feeding a commercial or a home made diet? If it's commercial, it's probably nutritionally balanced, but it's a good idea to let the vet know exactly what you're feeding, just to be sure. And of course give plenty of water. There are some foods that are more conducive to calcium crystal formation than others, and I'm sure your vet will go over that with you.
The antibiotics might be a good idea. So is the urine culture. To get a good x-ray might require Sophie to be sedated, so that's a little more complicated, so if cost is an issue, you might want to ask the vet if they think it's necessary first. You probably have some time to see if the crystals resolve on their own before you need to make a decision about the prescription urinary diet, but again be sure to tell the vet exactly what you're feeding Sophie now to see if that could be causing the problem.
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