My parents insisted on flying us all to Las Vegas when my son was 6 months ( not that I’m complaining, mind you! 
But I was wary of travelling by air with such a young child) After the flight, it was mentioned to me by a passenger that he had “been really concerned when he saw there was an infant on the flight, but was pleasantly surprised to have had an enjoyable trip”. He thanked me for having a “well behaved infant”.
I remember smiling politely and thanking him, while inside totally seething that anyone would say such a thing. As if any parent can completely control what pain or suffering an infant might have during flight! My goal was to eliminate as much inconvenience to other passengers, but aside from that, I knew I could only do the best I could. Perhaps I was lucky, and my son seems to be a “natural” at flying. 
At any rate, here are some of the things we did to try and alleviate other passengers’ discomfort:
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I got lucky, and the flight wasn’t full. I spent a good deal of time in the BACK of the plane in empty seats there. The Stewardess was kind enough after takeoff to direct me to some empty seats to care for him when he needed extra attention. While this did seperate me from the rest of my family during flight, I was welcome to move between the two seats when we needed a little more privacy for changing, feeding, etc. I would say to contact the airline to try and find seats in the BACK, rather than the front. The back puts you closer to the restrooms, as well. Nowadays, it’s tough to find a flight that isn’t booked to the gills, but less booked flight may also turn out to be your cheapest! perhaps a double bonus.
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We flew close to sleeping time for the baby. My son was one of the lucky ones who had a pretty regular schedule. He slept at fairly regular intervals. official “nap time” was about 2pm, official “sleep time” for him seemed to be between 9pm and 6am. our flight was at about 4pm. We deliberately kept him awake during his normal nap time, and he slept through takeoff. He did whine a little (I’m assuming from the ear popping), but happily sucked on my pinkie during takeoff with nary a peep. He woke up mid-flight, ready to party.
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A diaper bag with as many of his/her favorite toys as you can get away with, preferably travel sized. Does he have a book he enjoys when you read to him? bring it. Something he’s used to playing with in the afternoon? Bring it.
In short, anything we normally did during the day while NOT on a plane, we did on the plane, more or less on schedule. It seemed to alleviate problems. If the atmosphere was new and different, he didn’t seem to notice or mind. I did try to show him what the view looked like out the window, but at 6 months, I don’t think he cared much. it was -MY- first plane trip too, though.
Various teething cookies, regular feedings, and basically not breaking much from the normal routine seemed to help. If you’re in the air at 4, and 4 is when you usually give a treat, do it. If you’re in the air at 6, and 6 is usually nap time, vacate to as quiet a spot as you can, and try and get them to nap. DEFINATELY have something available to suck on during takeoff and landing. My son was not nursing then, so I made sure to have a bottle prepped, a nuk and any available body parts ready at hand. (IE: my pinkie, during takeoff)
Those things seemed to work for us without medications. The flght from where we took off was about 2.5 hours. Yours may be longer. If you think medicating might help, I suggest you speak with your child’s doctor about the best route. He/She already has a history of your child’s medical background, and may be able to suggest an over the counter medication to help him sleep through the trip.
The Benadryl idea is not a bad one. Apparently, that’s how my younger brother made it through a plane trip that my parents needed to take him on, but it was suggested by the family doctor, who had a medical history in front of him when he suggested it. I would caution against using medication to make a child sleepy in flight without double checking with your child’s doctor first. And in this day and age of technology, perhaps the doctor will have a better solution.
