You may have some choices. You can get a prescription from your M.D. for an INR Test Machine and for the supplies, or you can go the route that some others here have - and contacted the services that charge an arm and a leg for sending you the machine and reminding you to to your testing (and then THEY inform the doctor of your values), or you can consider buying your own meter and supplies. Some vendors will sell without a prescription - but I can't advise this, because the forum rules may not allow it.
For myself - I've bought my machines from vendors on e-Bay. I've had a doctor friend buy the strips for one of my machines - saving me a fair amount of money; and I've bought the test strips on eBay, and I've had a good experience with the machines and supplies bought both ways. Sure, it would be great to have the insurance pay for all or part of your testing, but if they are unwilling to help, or make you jump through more hoops than you want, etc., it may be worth just considering alternate sources if there are no acceptable options.
With no insurance, I am extremely grateful that I've been able to go the self-testing route, fairly affordably.