God bless you for giving this sweet baby a loving home! I think you are doing the wise thing by taking her to the vet and getting to the bottom of this. I am at a loss as to what may be wrong. The only suggestion I might add is to try her on yogurt or cottage cheese instead of the ice cream.
It's really hard to tell them no when they want ice cream ... my little "fatty" is the same way! Please update us after she sees the vet.