I have a very oily cough and thick mucus after eating a dairy product. What should I do?

Hello :) I am writing to you because for a very long time I have had a really fatty cough after eating one or more dairy products or something that contains them (for example a dish with béchamel). As I get older I realize that it is getting worse. I have very fatty coughing fits and I have to spit and clear my throat to expel this thick "mucus" to avoid choking. It became a handicap in my daily life. I am a hypnotherapist and trainer so I have to anticipate and not take an appointment before half an hour after eating because my voice is too hoarse and I cough. Thank you for enlightening me on all this because I don't know what to do.