Takeoff and landing are the crucial times because of the changing air pressure and a child’s not being adept at clearing their own ears. If the problem occurs at takeoff and the child stays uncomfortable during most/all of the flight, it’s no fun for the child, you, and your plane neighbors. I’ve seen and heard it. No fun at all.
To help avoid this, time it so the child is hungry during takeoff and landing. Then, give food/snacks that require chewing and swallowing. This will help clear the ears.
You can also pull down gently on his/her ear lobes, which will help equalize the air pressure.
Before the flight, practice with the child to see if s/he can open their mouth as wide as possible. If the child is able to, this is another way to help equalize air pressure during takeoff/landing. (15 months, hmm, the child might be too young for this trick)
Bring small, new and interesting toys/gadgets the child has never ever seen before. If the child is uncomfortable, this is a way to distract them while you try the other things. If the child is fine, keep the toys for if needed at landing, or for the return flight. By “new” that means new to the child, not necessarily brand-new. Something different.
I second the suggestion to use Benadryl as a sleep aid. No, do not try the sleep deprivation, that could backfire badly on you.
I also like the suggestion of handing out foam earplugs with a smile. It’s mostly a gimmick, to be sure, but goes a long way in establishing friendly neighbor relations. They’re inexpensive, too, at about $4.00 for 10 pair - here is just one example.
Good luck!