It might be helpful to talk to your doctor further about this, to see if your employer can help you with desensitising your fears. I used to be terrified of lifts - I'm still not comfortable - but when I worked on the 7th floor I just had to make myself get over it, I couldn't manage all those stairs. However - your getting stuck is not so much an irrational phobia, more a real fear of it happening again, I can't think of anything worse ;-(
Try to do it one floor at a time, always having someone with you who understands - it can work, but I know how scary it is.