Does Cefuroxime Axetil Take More Than A Day To Work For Severe Cough And Swollen Lymph Nodes?

My dr gave me cefuroximeaxetil for uncontrollable coughing and mucus draining in back of throat I have swollen lymph nodes in my neck i was on the medicine 1 day . This morning I woke up coughing . Can you Tel me if this medicine takes more than a day to start work and Is an antibiotic the right medicine for an uncontrolled cough. I had my first covid vaccine 2 weeks ago.