I’m coughing phlegm up every morning around 11

Basic stats: I’m 31f, 5ft tall and 180 lbs, I take Zoloft and birth control pills daily and an albuterol sulfate inhaler as needed for asthma.

For the last 10 months or so, I’ve been coughing up phlegm around 10-11am, usually when I’m getting ready for work. The sputum is a normal color like greenish beige I guess? Not the kind of yellow or green I get when I’m sick. I usually end up coughing out about a tbsp’s worth in total. I had a video appointment with my GP and first he thought it was a long term infection and gave me antibiotics, but nothing changed. Then he said maybe it’s something related to my asthma and advised me to take my inhaler right before I go to bed and when I wake up. No change. I’m gonna get a second opinion but I want to see if there’s anything obvious I’m missing. I have no other symptoms like runny nose or fever or sore throat.