I don’t think Carly was claustrophobic, per se, but it was the closed elevator bringing back memories of being buried in that casket that brought on the panic attack. I think if I had been buried like that, I’d end up, not just claustrophobic, but insane…well, more insane than I already am. 
I just can’t imagine how horrific something like that would be.
BTW, I’m not claustrophobic at all but I could very well lose it when I have to have an MRI. I have to keep my eyes closed and think about something pleasant.