Is it possible to not have enough fat for fat injections for my face?

For full face fat transfer procedures, I usually graft between 30-50 cc of fat - I have never encountered a patient that did not have adequate fat donor sites for facial fat grafting procedures.

In general not a lot of fat is needed for grafting to the face.  Most patients have some along with outer thighs. However there is a small chance that you don't have enough depending of how skinny you are.  Without an exam or at least pictures its really hard to comment on your specific case.