Most doctors are very eager to prescribe blood thinners so if your
doctor says you are outside of the recommendation range I think you can believe him.

Do you take any nutritional supplements? A very common combination, fish oil for the omega-3 DHA and EPA and curcumin as a general anti-inflammatory, are good for healthy people too and may have much the same effect as blood thinners when it comes to avoiding clotting issues. Others take the route of a baby aspirin per day, but that's rather less popular now than some years ago.

Other nutritionals offer additional and alternate approaches, too, you can have a new hobby good for years just researching them. What I've never seen, however, is a comparison to prescription approaches!