Depending how bad your anxiety is you should talk to your doctor and get medication for the flight. My grandfather has to do this when he flies. My mom on the other hand is just a nervous flyer and 2 glass of wine are enough for her.
Anxiety often doesn't respond to logic, but you are statistically safer in a plane than in a car.
I'd talk to your doctor or a therapist for ways to handle the anxiety for sure. Other than that, I'd just be prepared. Pinterest has a ton of posts & there are a ton of posts online on things to carry on to keep you occupied (preloaded movies on a tablet) like noise cancelling headphones, ginger chews for nausea, good snacks, what to wear to be comfortable, etc.
I have a fear of flying myself but also get motion sickness. I bought Dramamine which is too help with motion sickness but the plus side is that it causes drowsiness so it actually caused me to fall right to sleep and next thing I knew we were landing. Even if you don't get motion sickness it might be good to take just so you can sleep through the flight. They sell them at the airport or you can find it for cheaper at like CVS, walmart, target, etc.
I get super anxious about flying because I get SUPER motion sick.
I use sea bands (the wrist bands for motion sickness), dramamine, and I also tend to wear myself out with no/little sleep, and I don't eat much, either. Add in gum for takeoff/landing, and DH says I end up sleeping much of the flight.