If you cool your sandwich completely on a rack, as was suggested, it will help eliminate some of the sogginess problem.
I’d also take the extra measure of wrapping your sandwich (after it’s cooled completely) in parchment paper, or at least a paper towel. This will help a bit to wick away residual moisture and soak up some excess fat that may cause even more sogginess. That said, as the previous answerer stated, the only thing that’ll bring your sandwich back to crispness would be a re-heat.
The other answer would be to make a calzone instead of a grilled cheese. You can use pre-made pizza dough, even that “little doughboy” (you know who I mean) pressure packed pizza dough in a tube. It’s baked, not fried, so you’ll get something that has a longer crunch life, if you don’t use any very wet ingredients to stuff it.
Last suggestion: if you’ve got a toaster oven where you’re planning on lunching, assemble the sandwich but don’t cook it. Wait til you get to school, or work, or wherever, and grill the sammie on site!