No, a .org website is not always a reliable source.
Websites are fantastic sources but they depend. Ones like the Mayo Clinic are health-certified, I advise you to check that out.
Another one is a university website, universities are always reliable. Ones like Harvard, Oxford, etc provide reliable health informations
Last, check the link URL. If the website has a .com, it could be reliable. If it has a .org, it could be reliable but isn’t always. If it has a .gov, that is reliable and is government certified.