Is an asprin going down the wrong pipe need for concern?

A short time ago I was taking two aspirin and one went down the wrong pipe. I immediately started coughing and my wind pipe was burning from the acid in the pill. After about 5 minutes I coughed up about ½ of what was left of the tablet. Now I have a terrible cough and my wind pipe is very irritated. Is there anything I should do? Do I need to go to the doctor or because I coughed it out is this just my body’s response to an irritant.