Can I do massage to my face after fat transfer to face?

Avoid massaging. No, you need to avoid stressing the fat injection area for three weeks. No rubbing at all for the first two weeks, only really soft and gentle washing. For a fat graft to be successful, it takes two to three weeks for the extracellular matrix surrounding the fat graft to reach enough strength to withstand minor stresses.
Yes and no. You need to check with your surgeon to see if its ok. Most surgeons advocate some massage after surgery but it depends on where the fat was placed and how.