I was put on lasix for shortness of breath, is that a common practice?

If the doctor felt that there was fluid in your lungs then yes it would be right to give you Lasix. Were you given anything else?

Lasix (furosemide) is a loop diuretic (water pill) that prevents your body from absorbing too much salt, allowing the salt to instead be passed in your urine.

https://www.drugs.com/cg/pulmonary-edema.html

https://www.drugs.com/lasix.html