Would fat transfer help inverted nipple and breast asymmetry caused by recent surgical removal of benign cysts?

Yes, fat transfer can help in a great deal of situations similar to the one you described.  However, the answer really depends upon a physical exam in-person.Best of luck!
Dr. SubbioBoard-Certified Plastic SurgeonNewtown Square/Philadelphia, PA

photos would be very helpful to assess the asymmetry - re the nipples there is a chance because of volume pushing nipple out but it's unpredictable

If you did not have an inverted nipple prior to the cyst removal it is likely being caused by tethered scar tissue. This tissue should be released to allow your nipple to project. Fat grafting to the breast where the benign cysts were removed can increase in size ~1 cup size or 150cc with fat grafting.