Hi Jacustomer-lrva2yen~

Technically yes and no.

The prednisone itself wouldn't be likely to cause this kind of swelling and subsequent licking. However, Prednisone (just like all steroids) causes the dog to become more thirsty than usual, which makes them drink more, and eventually urinate more.

It's possible if your girl has been asking to go outside more often today, she could have made herself a little uncomfortable from the acidity of the urine. Of course being uncomfortable makes them lick more, so that could be the cause.

Since it's only started today, I think it's okay to just monitor it for tonight, but if it's still bothering her tomorrow, or if she starts having other symptoms such as blood in the urine or any sort of purulent (pus) material, then you should have her seen as soon as possible...just to be on the safe side.

I hope this helps.