I was diagnosed with strep last week, i finished antibiotics but still have white residue in back of throat. if doesnt hurt but will those patches go away? its been over one week. maybe frequent salt water gargles?

You can certainly try gargling with salt water as that may help. Also, if you had a viral illness at the same time or tonsillitis from strep the white patches may last a few weeks even after you are finished with the antibiotics. Your glands may also be swollen and that can also last. If the pain returns or a fever develops or any difficulty swallowing, please see your doctor again.