Can a solid diet pass through the windpipe without making the person cough?

Hi doctor,

Today I was eating lunch and felt something weird. I was chewing food and took a bigger bite than I thought. To break it down, I was chewing and had food on the left side of my mouth as well as the right side of my mouth. I tried swallowing some food in the middle to open more room in my mouth while still having food on both sides. The food slid down my throat when I swallowed, but it felt weird. It did not feel like it went down the right way. I did not cough or anything, so I thought I was fine. A few minutes later, I felt like I had something lodged in my throat, and now I have a weird feeling on the right side of my chest. I also have trouble breathing a little, and my voice does not feel like it is projecting correctly. I feel the slight need to throw up as well. I have not had any problems swallowing in the past. Could the food have gone down my windpipe and into my lungs so quickly without making me cough? And if it did go through my windpipe, could the chunk of food have damaged my vocal cords?