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. 

Fat grafting is an excellent tool in improving the appearance of assymetry/contour issues after previous breast surgery.  Inverted nipples can be addressed through small incisions near the nipple to increase projection.  Fat or a dermal graft can be used as an adjunct to help maintain nipple volume/projection.

If your nipple inverted after the removal of the cysts, then a fat transfer could be helpful to fill in that area. If your nipple was inverted prior, no, the fat transfer would probably not make much change. I would suggest meeting with a board certified plastic surgeon and discussing your options.

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Certainly fat grafting to areas of breast excision will help to some degree but blood supply due to surgical scarring may limit grafting success. Nipple inversion is best treated with nipple eversion surgery. I highly recommend you see an ASPS surgeon who can completely asses your situation and provide with multiple viable alternatives