No more laying on back😖

My sons pediatrician told me that he cannot sleep on his back anymore due to the back of his head being flat. They’re taking measurements of his head soon. He’s 4 months and I was always told to lay them on their back to sleep. However he still won’t sleep without being swaddled. I’m terrified to lay him on his sides or stomach and then SIDS happen. I was told to put a pillow on the side so he won’t lay on his back. I haven’t been able to sleep Bc I’m constantly checking on him and his breathing. Any advice