i wouldnt purposely sleep on your back this far along, you dont have to sleep right on your side, you can get a pillow and just have it under a hip so you are still kinda on you back but at an angle... in the hospital they put a wedge pillow under one side so your not flat on your back but not on your side so i dont see why you can do this at home.. ive been starting this and its been better than last time lol also i put a long pillow on one side a and a flat pillow on the other and when i angle on one side i put the pillow against my tummy so it doesnt pull the ligaments from the other side (if this makes sense lol) either way both sides are supported and its pretty comfy... but definitely pillows are key!! PS im almost 17 weeks :)
no, you aren't hurting the baby.
your body wakes you up for a reason, to shift over cause you're uncomfortable, or baby is uncomfortable. as long as you listen to your body and don't force yourself to stay in a position that is uncomfortable you are fine.
things will change for you again later and you will probably want to be on your side. you can always try to put some pillows behind you so you can't roll onto your back, if it worries you that it is hurting baby.
and yes, left side sleeping is said to be best later on.
but right now i think you are fine. hope you find a nice comfy position, later it will be much harder to find and keep. ; )
best of luck!