sick newborn

i feel so bad. My LO isn't even 3weeks old yet n he has a cold. I'm a FTM and i have no idea what to do for a sick newborn. ive taken him to the doctor and they said there is nothing i can do but watch him and monitor it. He's still eating its his sleeping that's being disturbed. when he's on his back he seems to be weighted down so he ends up sleeping or napping on either my husbands or my chest. My MIL said to bundle him up and let him sweat it out. but considering its tends to be in the negatives over here. im afraid it'll turn into the flu or worst listening to her

I feel bad but idk what to do any ideas mommy's?