If you are worried about your breathing you should speak to your doctor.
I had a feeling like this after long or intense rides, although it felt more like I couldn’t exhale fully without wheezing or coughing which limited me to shallow breaths. Eventually I went to the doctor. After a few months of monitoring my breathing through daily peak flow tests I was diagnosed with asthma. I am now on a daily steroid inhaler which almost completely removes those symptoms.