Baby with flat area on head?

So I took my 4 month old to the doctor for her regular check up and he noticed the right side of her head in the back is kind of flat. She prefers to sleep facing to the right and I never thought anything of it until now. He said I need to have her sleep looking to the left. When she falls asleep I try to turn her head but I notice when I wake up to check on her she is back in her same old position. I won't let her sleep on her tummy at night due to SIDS and I am afraid to prop her on her side with a blanket wedged behind her for fear she may pull it over her head or turn into it and suffocate. The doctor informed me that if it doesn't improve within a month he wants to have her fitted with a cranial helmet that she will have to wear 23 hours a day. I don't want to put her through that. So does anyone have any suggestions? Has anyone else dealt with this same thing in their child?