Ball of mucus stuck in my throat

For the past 3 weeks I have been coughing pretty badly.  I can tell there is mucus in my throat also.  It feels like I have a ball stuck in my throat.  2 weeks ago I went to the doctor after taking Mucinex D for a week with no relief.  Now my doctor at this point had seen my brother about 3 times for the same thing and he had no clue what was wrong with either of us.  Like my brother, he gave me the z pack.  He also wrote up orders for both of us to have a throat culture done.  My brother’s results came back normal last Friday, I haven’t gone for mine since I’m waiting for my insurance card to come in the mail.  My brother is going to see a specialist this Thursday but we both can’t take this anymore.  We cough so badly trying to get the mucus out but usually we end up not being able to breath and gasping for air.  We have both thrown up with no relief, we still cough and find we have a ball of mucus in our throat.  What is this and how can we get rid of it??  I have a 2 year old daughter that is already coughing but isn’t bad but still, I don’t want her to get whatever I have.  Please someone give me some advise as to what is wrong with me and how I can get rid of it!!