Who should I inform of my anxiety disorder to make this 18-hour plane trip easier?

When are you. scheduled to fly? If you have a couple of weeks, I would suggest contacting a psychologist to develop a progressive desensitization treatment plan. It involves teaching you a relaxation technique and developing a hierarchy of your anxiety about the flight. Then you imagine the flight (from the least anxiety to most) while relaxed. Some airlines offer assistance to people with fear of flying.
Doctor. You may find that your doctor can help, if you speak openly with him/her. .
See below. Your fp/pcp or a psychiatrist can evaluate you & may prescribe an anxiolytic ("nerve pill" to use before & during the flight. Alerting one of the flight personnel to your condition will let staff assist you if needed. Involve yourself in reading, watching movie, listening to music, chatting with neighbors to distract self from worries during flight.
See your MD. Consult a psychiatrist before the trip. He/she may give you medication to diminish anxiety and also help you sleep on the flight. If you will be flying with someone tell them about your anxiety and ask if they can help you.