The goal of this clinical trial is to evaluate the effectiveness and safety of mesenchymal stem cell therapy in long-COVID patients. The main questions it aims to answer include: * whether umbilical cord mesenchymal stem cell therapy does benefit long-COVID patients * whether umbilical cord mesenchymal stem cell therapy is safe for long-COVID patients. Participants' demographics, chief complaints, and vital signs will be collected and recorded. Basic physical examinations, bloodwork routine, biochemical indexes, oxygen saturation (SpO2) levels, 6-minute walk tests, high-resolution computed tomography (HRCT) scan (if necessary) results will be conducted. Participants will receive either an intravenous infusion of mesenchymal stem cells, or a placebo for one time. Participants' symptoms will be assessed on Day 28 of the trial. If there is no significant effect, an additional infusion will be given on Days 35-42, and the symptoms will be reassessed 28 days after that. Continuous nebulized inhalation of UCMSC-derived exosomes will be administered for 5 days twice daily to treatment group, with no treatment given to the control group. Researchers will compare data and information collected from the treatment and control groups to evaluate the safety and efficacy of UCMSC-derived exosomes for the treatment of chronic cough after COVID-19 infection.