There are a variety of sources of biographical information on medical practitioners in England, but I will focus on those that are relevant to find out more about John Van Cooten.
The Cyndi’s List category for doctors contains some useful links for online resources, but paper resources are still significant. The British Medical Association has an excellent page detailing information sources. Alex Glendinning’s “Was Your Ancestor a Doctor” provides important background and sources. The Royal College of General Practitioners “Tracing Your Medical Ancestors” page is good.
John Van Cooten was in practice from about the early 1800s to about the 1840s possibly on Guernsey for all of this time. I have yet to consult the Medical Directory. This directory commenced publication in 1845, so an unsuccessful search may not mean much. The genealogical collection of the State Library of Victoria holds copies on microfiche for 1848-1869. The GSV Library holds a copy on microfiche for 1847.
I have consulted the University Alumni documents for both Oxford and Cambridge with no result. I need to find publications for other Universities active in the early 1800s.
I have searched W. Munk, Roll of the Royal College of Physicians both in hard copy at the University of Melbourne, and on line without success. Unfortunately Munk covers Fellows only for 1826-1997, and it is probable that John was not a Fellow.