My first problem was convincing my doctor that salivary stones exist. Hopefully you don't have that problem, but I have serious concerns about using steroids to break up a stone. You are certain that your doctor agrees with you/told you that you have salivary stone(s)? I'm kidding, but I would ask if you have any doubts.
They are for real, in case you need reassurance. My mouth is watering as I write this, the memory of the stones I have passed, spit or whatever the term should be, is vivid. Most stones popped out during a yawn. I've tried to force a yawn and so far I haven't been able to excise a gritty pearl. Something tells me that the stone is seriously stuck, even being walled in by the body, which can happen. You may find a dentist is better equipped and familiar with removal of salivary stones. The surgery, if you require it, is usually a small cut to widen the usual opening, closed with a single stitch.
My PCP removed a couple of stones from the sublingual salivary glands and my dentist popped one from one of the maxillary salivary glands. He used his suction tube with a special tip and aside from the feeling that the stone was in my ear, it was more or less painless.
I'm guessing that your doctor knows what she/he is doing. My experience has been more of a manual stretching of the salivary gland opening to remove the stones. One story told me by a nurse at my CF clinic shocked me, but gave me ideas. While at her dentist one time, an air jet was accidentally pointed at the orifice of an upper salivary gland. It immediately inflated, and it was very painful, I'm sure, but she reported having a lingering sludge that drained for a day or so. I wonder if any fluid could be washed into the salivary gland.
The usual method for small stones could work for you. Sucking on a lemon and keeping extra hydrated along with massaging the suspected gland is effective. Some super salivation over an extended period is your best and probably last do it yourself fix.
Good luck, don't overdo it,
LL