belly sleeping -calling all opinions

Sh
My son is two months and has not wanted to sleep on his back since day 1 in the hospital. I tried for a good month to continue to put him on his back every time he went to sleep and he would continue to wake up and scream. I even let him cry it out for a little bit but being so young I thought the cry out method wasn't necessary at that point. Now he sleeps on his stomach because he has rolled over multiple times to his back and he can lift his head side to side. He always makes tons of noises while asleep, so since I'm aware of everything now and every noise I am always checking on him. This has nothing to do with me getting any sleep either, I would stay up 24 hours a day for him. I just want him to be comfortable and to get the sleep he needs. The pediatrician isn't happy with me that I let the baby sleep on his stomach. What has everyone else done in this situation and should I just continue to do what's best for my child?