Pressing on,
Like Bodoni says, things can get dragged out or trapped in the valve during intubation and migrate their way out on their own, it happens to me often. I have a crook in my valve (like an elbow) and things just get stuck in their...About 1/2 later they pop right out (sometimes it is a tsp of gunk that slides out)...no biggie.
On the other hand, things can also get stuck further down the canal and partially block the tube open and then allow air or 'stuff' to come out unexpectedly.
It the gas came out before the carrot then you are cool...it was probably that that allowed the gas out, if it was at another time afterwards then maybe you need to do a simple test.
Fill the tub with water, submerge yourself. If you see air bubbles popping up or out then you have a leak, if not then you may be just fine. You can try it again a week or two later...For now, do not forget to chew your food well.
Sharon