When you choke, the thing that your choking on is being stuck in your windpipe and is not going down the right way. If you have swallowed whatever you were choking on, it has most likely gone back up the windpipe and down your esophagus which is the normal way to swallow something. It is impossible that whatever you swallowed went into your lungs because if it did, you would not be able to breathe and would most likely suffocate. if it went down your stomach, it should digest OK BUT if the thing that was swallowed was sharp or quite large than immediately seek medical help.
It won't go in your lungs ur. You would choke on it.
If you swallowed it and it ended up in your lung, then you have a real problem. That means there is a hole in your stomach that leads to your lung.