Have you tried different ways of tummy time instead of it being a cushion type? xxx
My little guy (4 months plus one week) was exactly the same. He could move both sides but always slept on right side. If we moved his head to the left when sleeping he just moved back to the right. We made a big effort to make sure we stayed on his left hand side when playing with him, putting toys to his left etc and in the last couple of weeks he has started sleeping on both sides. It took persistence but we got there so keep at it!
For tummy time, have you looked up other methods like over a pillow/rolled up towel, on your chest or on your lap? When he’s lying on his play mat, if you move a toy above him does he move his head both ways to follow it? If not, he may potentially have some tightness in his neck which is causing him to have a strong preference for lying on one side. It could be worth taking him to an osteopath to check this as they are able to release any tension using very gentle methods :)
My baby is almost 4 months and has always slept on her right side. I asked the health visitor and she said its fine and she should grow out of the flattness as her skull grows x
I had this problem with both of mine, my eldest had this and mentioned it to my HV, she said it's totally normal and he is perfectly fine now xxx