Both a chesty and tickly cough?

What you have is called an acute exacerbation of asthma. Your cough seems to be severe enough to meet your doctor this time. Having yellow means that there is infection (bronchitis or pneumonia). You may need a chest radiograph to be done and need to take asthma medicines like salbutamol inhaler and antibiotic tablets. So please do meet your Pulmonologist soon.