I feel your pain. Coughing is so disruptive and everyone around you thinks you're ill with some contagion. I've gotten into the habit of clearing before I leave the house for any event. I also keep a supply of Luden's Wild Cherry lozenges in my pocket. According to Sue, the pectin in the lozenges help with coughing. I have found this to be true as long as I have also cleared my lungs. It's amazing, even the smallest amount of mucus/phlegm seems to cause coughing. Talking also leads to coughing for me. Dr. McShane (airway clearance video posted on this site) explains why.

Since you are coughing so much I would suggest increasing the nebulization with 7% saline to 2 times a day. First thing in a.m. and then again in p.m. If you find you're too tired for the p.m. try to squeeze it in around 4pm before dinner prep etc. Then you could try some ACoB or AD before bed. It takes time to perfect your technique. Personally, I would be proactive to remove airway mucus and not depend on coughing fits as airway clearance.

What has worked well for me especially is autogenic drainage. I used to use the AD app but I found that was a waste of time after consulting with a RT. I no longer use aerobika, unless I get desperate.

Start here if you have not learned autogenic drainage. Hope this is somewhat helpful.
https://bronchiectasis.com.au/resources/airway-clearance-videos
PS - I know there are differing opinions on exercise replacing airway clearance. Some people can get away with this substitution. I am not one of those. My very experienced RT who has worked with CF and bronchiectasis for decades says a resounding no, but maybe you will be among the people who can get away with it.

I told my DR. I didn't want to go out either because of the cough. He prescribed me a pill called Benzonatate 200 mg. It doesn't make me sleepy or loopy. He told me to take 1 hour before I go out. Was able to go to dinner and dancing without that cough. I am sure that it would not be good to take it every day because we need to get up the mucus but he wanted to help me be able to go out with my husband and friends to a concert or dinner without that nagging embarrassing cough. It worked. I have only used it a couple of times. I am cautious with it.

So glad you asked this question with your explanation of how things are for you. I was somewhat under the impression I was the only one with the all day problem.
Yes, mornings begin with much need to clear the sputum. I also nearly cough all day long and as well have to clear the sputum when I wake up at night. I wake up at least three times a night. Hard to know if it is my bladder awaking me or the sputum that comes up to my throat. For me, I chew tiny piece(s) of stick gum (throughout the day and for a while upon waking at night before going back to sleep) and it seems to loosen it all and helps me get what I can up and out before trying to fall back to sleep. My choice of gum is the Extra Polar Ice. Never have I chewed gum but, for me, it does give me some relief...not sure why. I chew the heck out of the small piece of gum and try not to have more than a stick and a half within 24 hours. I don't drink water through the night with one reason being the possibility of GERD/Acid Reflux and another reason, water seems to cause more mucus to form and the need to clear out the sputum.
I find it all is worse after I eat, and I understand that a couple others mentioned in another thread, it being worse after eating.
I have noticed that after the day of all I have done I bring up more mucus plugs early evening.
Yes, it does cause one to hesitate from being with others and I hope with time and all we do to help clear the lungs daily, that will change.

The local pulmonologist I "ran" to first in my journey to find a pulmonologist specializing in BE, Bronchiectasis, also did not mention anything to do other than to buy a PEP devise and learn to use it. He did not mention nebulizing or any method to clear the lungs of the mucus/sputum.

How long have you been doing the routine you started with? I find it has taken me much time to find my way to what is best for me. I am still learning with the help of those here on Mayo.
Is it worse for you after eating?
Have you had to take antibiotics for a MAC infection?
Barbara