Toddler has been the worst sleeper since day one

BoyMommy19 • Mommy to one beautiful baby boy born November 2019 💙

My almost two year old has not slept a full night since I took him home from the hospital. They say obviously newborns wake up through the night for feeding and diaper change but he has been waking up for bottles and diaper changes until now. He drinks about 4-5 bottles a night and if he doesn't get his bottle he screams bloody murder until he projectile vomits which is why I give in. Once he gets the bottle he falls back asleep right away. However when he is sick he won't sleep at all. He would just cry all night no matter what medication I give him. He cries of pain and being uncomfortable, not able to breath from nose, sore throat, fever etc. I give tylenol to lower fever and help with pain but it helps for a very short time and I can't keep giving him tylenol because it can cause liver damage after using 5 times in 24 hours. So to sum up everything no matter what's going on my toddler is almost 2 and a very very bad sleeper. I hear most parents say their kids sleep well through out the night with no issues. The pediatrician isn't any help btw so I gave up on his input. Do kids eventually grow out of this??? I don't want to force anything but would like tips to try or at least know one day he won't ask for a bottle all night.