I would definitely take pills after using the cough assist and not the other way round. Food and pills often gets lodged in my throat or on the back of my tongue. Sometimes I’m totally unaware that they’re there.
I’m not medically qualified, but it sounds more like the after effects of COVID to me too. I have never heard of the repetition of words being an early symptom. You say your neurologist thinks it’s nothing. Think I’d respect his/her opinion and stop worrying. If you can‘t do, that speak to...