I am feeling something stuck in my throat with shortness of breath. What is this?

Allergy? Sounds like a pulmonary allergy. Seek care with a medical doctor.
Several ideas. Shortness of breath and the sensation of something stuck in your throat Could be due to 1) infection (epiglottitis) 2) psychiatric (globus reaction) 3) developmental anomaly (outpouchiing of the esophagus) and others. The best thing to do is to see a doctor so that one can do testing depending on your history, present illness, and physical findings.