I got the shot at 32 weeks when I was hospitalized with preeclampsia. The doc didn't even discuss it with me, the nurse just came in the first night with the shot. I was freaked out too! Not about the shot, I understood what it was for, but that they thought I needed it! Like the PP's said, it's more of a precaution. No harm to do it but big benefit if it's really needed for prematurity. I didn't have any side effects and ended up carrying my girls to 35.5 weeks.
I had a big growth difference between my girls. DD1 was 4lb 3 oz at 35w5d and DD2 was 5lb 8 oz. But they were both healthy and came home with me in 2 days. No NICU time at all. Still DD1 is smaller than DD2 which helps with clothes since they wear different sizes. Other than that she's just fine. Good luck!