Can my new doctors get my information from my old doctors if I don't want them to?

Probably Not. In the United States, for one medical office to send records to another generally requires the patient's signature. Note that if you see a new doctor within the same large practice (even if the physical address is different) you may have already signed a sharing agreement within that practice. The larger question is why would a person want to withhold information from a doctor?
Why? Why would you not want your doctor to have your medical history? The more information we have about our patients, the better we can treat! doctors keep everything in confidence. Trust your doctor or get a different dr.