Why not google restaurant names and put their numbers in your book? Then, as you travel, you can call for directions and take a break. Or make note of organizations that provide assistance, or hotlines you could contact.
Also, I know in FL you can call 911 nearly anywhere, and on the FL turnpike you can call *FHP (for Florida Highway Patrol) and get any assistance you need. Just tell them you have a panic disorder, as they are trained in special circumstances.
I'm sure you understand why ppl don't feel comfortable giving out their numbers to a stranger.