The head of the penis contains erectile tissue and fat should not be injected into this tissue as it might damage it. The fat is injected into the subcutaneous region of the shaft and does not affect the stiffness when the corpora are engorged. It is performed under local anesthesia. A mild sedative may be given prior to the procedure if the patient does not drive after discharge for at least 8 hours. No surgery is risk free.
Fat injection is very safe.
You can not be allergic to your own cells. Infection is possible but antibiotics are taken pre and post-op. Bruising and swelling are normal. The biggest problem is obtaining symmetry or evenness, but careful molding at the end of surgery and the possibility of future touch-ups make this less of a concern. Risks are outlined in detail in the Special Consent to Fat Injection Surgery .