Staying in  the position that your doctor instructed you to gives the procedure the best chance of success. Where I work we instruct patients to maintain positioning 55/60 minutes. That gives You time to use the bathroom, put in eye drops etc.
If you sleep on your back the bubble will not be in the right position. This lessens the chance of success and increases the chances of lens feathering and cataract if you are phakic. I would also ask your doctor to clarify if you have a retinal tear or retinal detachment. Based on your treatment and the mention of sub retinal fluid, it sounds more like a detachment to me.