Something that's very important to remember while in the middle of this... the screaming baby sounds much, much louder to you than it does to everyone else since it's yours and it's right in your face. And I discovered that really only the two rows directly surrounding you are seriously affected by your screaming kid. It's still a nightmare (especially for those poor people), but it's not as bad as it would be if you were stuck in a similarly sized room with your screaming child and all those trapped people.

The airplane noise really drowns out a lot of it. On our first flight back from Florida with my then 9 month old, he went hysterical for quite a while. I was so embarrassed and upset and frustrated and trying to settle him down... then we got off the plane and people several rows up were complimenting me on what a good baby he was and how they never heard a peep from him.

Also remember that the majority of other people on the plane have or had small children at some point and know what it's like to be in that position.
That is very kind of you.
I travel for work and ALWAYS try to sleep (get some rest in the bank). Screaming children are not a pleasure - no matter how much you love children.
a GOOD example.....
A woman with a baby sat next to me on a 5 hour flight - my heart sank.
She opened her bag and produced....
A sippy cup for takeoff and landing to keep little ears popping
Quiet games and distractions to keep the little boy busy
Snacks to keep his tummy full
He was simply - perfect!
She had bought two seats and he sat between us. She also keep him busy at the airport before we boarded ---- I watched them walk around and play games. Diapers were changed just before boarding.
It was a PLEASURE to sit with them.
What was the difference, I suspect he was a well behaved little boy to begin with....but the mother took the responsibility to make sure he was fed, clean and entertained during the flight. When we was awake - he had plenty to do.
Another point about buying a second seat.
Why do you use a car seat when your precious baby is in the car? Because you have to by law or because you want to keep your baby as safe as possible?
Airplane cabins can be as gentle as a still pond....OR they can suffer from turbulance. You may find YOU are more comfortable knowing your toddler is snuggled in a travel/car seat and safe.....not to mention it is familliar and comfortable <--- that could be a good thing too!