Purchasing a no contract phone does NOT mean it is unlocked.
Unlocked iPhones in the US are sold only through the Apple store, did you purchase an unlocked iPhone from Apple?
If not, only the carrier can unlock the device and the carrier sets the terms and conditions under which they will unlock devices.
You bought a Sprint phone. Sprint phones are NOT unlocked. Sprint will only unlock the SIM slot for current Sprint customers in good standing for use while travelling internationally.
You bought the wrong phone. Since you're not a Sprint customer, you can not get it unlocked. Sell it to someone in the US and buy a phone you can use.