What costs and implications would be involved in travelling from scotland to usa to see a neurologist to try to get to the bottom of my health probs?

Health tourism: Good question. Are you sure a neurologist is what you want? Your health care costs would include c. $300 for a consultation, and more depending on the tests you may have done, such as blood tests, MRI, etc. Sometimes MRI sites can do their study for about $400. Most insurances, like Medicare, pay about $150 for the consultation, because they get a discount. Also add travel costs

Letter: I would recommend sending a letter to the DIrector of a Neurology clinic at a major medical center in Philadelphia or Boston. They can best direct the next step in arranging an appointment.