I had my twins at 35 weeks, they were bone fine though one was underweight and had to stay in hospital for a little while.
I had my first at 34+5, my waters broke and nothing could've stopped him. He was 4lb 7oz, perfect but small. He did have a three week hospital stay because he couldn't feed for himself. He just slept all the time which was to be expected given he shouldve still been in the womb. All babies are different though and it depends on how baby presents at birth as to whether any special care is needed. Best wishes :)
I had my son at 36 weeks and he was perfectly fine. You should be fine too, might just need an extra day in the hospital.