There is absolutely no risk of having Restylane at this point. Actually, the Restylane is a much better way of filling the lower eyelid than having fat transfer. The fat can lump, can't be adjusted, and many people are disappointed with fat grating because of the relative lack of long term results.
It is essential that you go to someone who knows what they are doing around the eyes. An oculoplastic surgeon is the right choice. However, it is advisable to see someone who does a lot of facial fillers and noninvasive treatments. In Baton Rouge, you might consider Jane Olson, M.D. She is a leading injector and has a national reputation for excellence.