I think your doctor is a little overdone on that point. The left side is ideal, because of the good blood flow to the baby, but being on your right side is certainly not going to harm your little one. I sleep that way all the time. Being on your back is not great, because the blood returning to your heart is impeded by the weight of your uterus resting on that main vessel, but if you happen to wake up that way, don't stress. Just turn a little, and go back to sleep. (If you can!) I've also slept with one hip up on a pillow to shift the weight off the centre of my body when lying on my back, if nothing else works. (I'm not really recommending that, but if you can't sleep any other way, then you could try that.)
Also, I sometimes find I have a much better sleep on the couch, because the cushions are softer, and I don't worry if I have to turn over. When I'm in bed, I worry about disturbing DH, and try to hold still. But on the couch, I can toss and turn to my heart's content. HTH!