A photo or video would be very helpful, vid moreso since we could hear the whistle and sputter.
The only faucets I've ever seen without an aerator are the basin farm-style spigots that have become a recent fad. All others should have one equipped when sold. That's an important distinction to make because many people remove them without replacing them, usually due to poor pressure or not wanting to be bothered to go buy another one. Your faucet could be missing one for that reason.