What could be causing my shortness of breath when I'm trying to fall asleep?

Many things. Shortness of breath when lying down could be due to heart issues. Asthma gets worse at night. Reflux could be aggravated by lying in a flat position. Obstructive sleep apnea is possible but would occur when you are sleeping. I recommend seeing your doctor.
Maybe asthma. Asthma can result in shortness of breath that occurs at night. Other symptoms with asthma include wheezing and chest tightness. Other causes of nighttime breathlessness include anxiety, panic attacks and acid reflux causing bronchospasm (narrowing of the airways).