A month ago i had covid and had this persistent cough for weeks dr said it was inflammation and had to use inhalers now i have a cold and started coughing again with phlegm this time , no fever but is this going to cause more harm on my lungs?

Covid-19 pulmonary infection causes significant post inflammatory pulmonary syndrome in some patients and I think you have that. Most of the time, the syndrome will resolve by times. If you have clear phlegm without fever or chest pain, you should be fine, take cough suppressant&expectorant (mucinex DM) if it bothers you a lot. If phlegm turns green or rusty color with fever, you need antibiotic.