I have flown, at times, numerous times in a year, and then there will be maybe 2 or 3 years without flying at all. What I've found is that there are all sorts of bumps and noises and such in a jet airplane, and they're all normal. But when you haven't flown, you don't know that. The wheels retract into the plane, there are these bump/thump noises, and you wonder "What was that!!??" But it's just the gear. Same with when they extend the flaps, or retract them. There's a whining noise you can sometimes hear when they deploy, but that's just normal.
Same with a little turbulence. You realize you've been through a few bumps before, the plane didn't fall out of the sky, and that's that. But if you haven't flown for a while, you don't know what's normal and what's not.
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I once flew into St. Louis on a little puddle-jumper, back before 9/11. They had a curtain between the cockpit and the passenger section. This day, they had the curtain pulled back and I could lean out into the aisle and look out the front of the plane. It was a bumpy day, very windy, and we were coming in to land in a bit of a crosswind. I was a little nervous, but I kept watching the pilots. They were having the time of their lives, or so it seemed. No concern at all, it was just normal.
Nice landing, everything was fine. I learned that worrying about it didn't accomplish anything except make me nervous, and I'd already decided to put myself in the hands of professional pilots. And they were.
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One thing you can do on the flight, if there's any bumpiness or anything, is ask your seatmate if that's normal. They'll tell you "yes," and you can watch the people around you to see if anyone else is nervous. You'll see most people ignoring everything that's happening.
Another thing I like is that some flights have an audio channel called the "Flight Deck" or something similar. It's the radio traffic from the plane to air traffic controllers. I think it's fun to listen and sometimes you'll catch a controller telling your pilot something like "Come right to heading 260" or some such, and you'll know you're turning before you feel the plane banking into that turn. I've found that on short flights that generally isn't available, but on long ones, much more likely. Try it, I think you'll find it fascinating.
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BTW: I also have a fear of heights--I hate movies where people are hanging off a tall building, climbing a sheer rock wall, like that. I hate that. I've been in the St. Louis Arch, at the top, and never again.
But for some reason, in a plane that goes away. I'm not exposed to the outside. I'm not getting vertigo, I'm just looking outside and marveling how it all looks from up there. BTW, look as you go over the middle US and see if you can spot any wind turbines. They look like little tinkertoys. I think they're funny as hell.
Consider getting all your media on a tablet, then bring a phat battery pack to keep it going all flight. I use this one: 
