I am not a doctor, I just had to mention that.
I have recently been suffering through similar symptoms, and since I live in Canada, I just went to a walk in clinic. As it turns out, what I have was similar to what my father had. (Our story is quite similar to your, dad got It then, I) my father only had the coughing, but I got the coughing along with the flu. My dad, after 3 weeks is done with the cough, just so you know the approximate timeline for the cough. I have only just been diagnosed with the flu and cough. You are probably vomiting, because you are coughing, and I have had the same coughing spazzes as you, what you should try to do, is get some over the counter medication, for simple dought and cold. Then wait out the flu. I hope this helps.