There are so many people who are claustrophobic. Have you ever seen a therapist for this, Anon?
I understand booking the flight, and trying to deal with your fear. That's a really fine step. But your fear about being on the plane and having a panic attack mid-flight will not help your fears, it might only make it worse. You are sort of self-treating by immersing yourself in a situation you can't get out of, and that may not be the best thing for you. Is this a flight for work or for recreation? Is it optional? What has been your reaction since you booked the flight?
I would suggest seeing a doctor before your flight and asking if you can have a small dose of anti-anxiety medicine, like Xanax, to take to help you through the flight.
Your boyfriend's apartment may be a better way to slowly expose yourself to what you are afraid of. I assume that you walk up because you are afraid of the elevator?
Do you think it would be possible for you to take the elevator for one floor? Knowing that the doors will open again in about 30 seconds and you can get off?
When one floor becomes possible, you could try two.
(He must be a good guy for you to walk up 20 flights of stairs!!)
Please know that 28 is not old, it's young. There are books on claustrophobia, or a therapist or counselor could probably help you in a few months.
You might be interested in this online claustrophobia support group. It's anonymous and free:
What sounds good to you as a next step?