That's because your intercostal muscles are responsible for expanding and contracting your ribcage to facilitate breathing.
Try not to do activities that make you breathe hard. Take it easy for a while.
If you smoke, right now you have some painful motivation to quit. The more and harder you cough, the longer it will take to heal.
If your lungs are congested you can take an expectorant such as guaifenesin to loosen up the mucus so you don't have to cough so hard or frequently.
If it hurts more when you inhale then it's likely a strained outer intercostal. Conversely, if it hurts more when you exhale then it's probably a strained inner intercostal.
Personally, I'd go see a doctor for some opioid pain meds.
