Yeah I second what Aerries stated. They unhinge their mouths in a way and after a meal you can sometimes see them re-align it back in place. If it was a respiratory issue, you would most likely hear some noises, like wheezing or such.
If you feed in the same tank, depending on the snake, you can put the mouse/rat on top of a papertowel to avoid any substrate eaten, but these guys are wild animals they get substrate in the wild all the time.

You should be fine, keep an eye out and congrats on the new guy! Make sure you're feeding the right size.