My doctor also gave my info for safer bedsharing. Because your sleep/sanity is important for safety too. We've also been working on Side-lay nursing. At 5 weeks mines still a little small to do it comfortably yet, but with my older one it was a naptime game changer.
If he is just like this for a short time and not usually, then he is probably going through a growth spurt or something else and needs the comfort. During the day you can look into carriers or wraps. For sleeping, if you have a comfy chair recliner, I have layed myself in pillows so I'm comfy and out baby square on my chest to sleep. No pillows near baby and kinda did a wrap so wouldn't fall off me. I also don't move much in my sleep. Not a long term solution. But if it's just for a shirt growth spurt, helps you and baby get rest
Look up the safe sleep 7. My first was like that and it saved my sanity.