Comfort feeding and SIDS?

B.

My 1 month old son is always nursing, and often he will comfort nurse and nap on me during the day. I don't really mind other than it scares me that he might not be getting enough oxygen or be able to breathe properly as he is on his side rather than a flat hard mattress on his back.

Is it safe for him to always be on me/be held? Often times I can get him down in his bassinet but there are other times where he fights it more.

Thank you.