This is almost certainly due to some unresolved trauma involving the throat and/or mouth such as choking or drowning, as breathing in through the mouth should be just as easy as breathing in through the nose. We may have a slight preference for one or the other, but if it causes a big reaction then there is something there to work with.

Try titrating the experience. Breathe in and out through the nose for a breath, then the mouth for a breath, then back to the nose for as long as it takes to settle, try again, etc. See if you can connect to the emotional quality of that feeling of constriction. What would it be like to say, or do, or express?

Another option is to titrate within the same breath. You can start breathing in through the nose, then switch to letting a bit in through the mouth halfway through the inhale, then back to the nose, all on the same inhale, and you can play with it the same way on the exhale.