R.,
Either side is okay to sleep on. Rather interesting to note: My mother's doctor never told her to sleep on her side. Mine didn't either - I got information from an EMT class and learned about the Snoogle at Babie's R Us. Had I had neither, I wouldn't have known.
Sleeping period didn't happen very much after 6 months for me ;) so I will tell you - either side is okay. Sleeping on your back can be uncomfortable, and it can cut off your blood supply returning to your heart. The baby rests on a lot of displaced organs when you are on your back, and when you tip yourself to the side - sometimes you can get away with just tipping your hips while your back is flat, but I didn't do it, I was so heavy I moved the pillow out of the way :| before I even fell asleep!
Snoogle or body pillow, if you fold it into an L-shape, put part between your thighs and the rest between your arms (snoogle comes up to rest under your head too), you shouldn't have body parts falling asleep.
Nothing is a guarantee, though, so if you still find it happening, contact either OB or your Dr. There may be something else up.
Sometimes I would fall asleep in a semi-reclining position. Since I can't roll anywhere that way, it wasn't bad. The only problem was falling asleep with the light on. What a pain!
Good Luck!
M.