Having just had a stroke, I don't think you should be choosing to not use a drug your doctor prescribed. Not sure when your followup appointment is, but I would call the doctor's office and let them know you would like to be prescribed a generic med that offers similar protection.
Getting blood work on the road is no problem. DH was on warfarin for over 10 years and he got prescriptions for the protime test when he went into the doctor. When he needed bloodwork, we looked up the nearest LabCorp, went in, handed them a prescription and they would fax the results to his doctor.
He no longer is on that med, but it worked well. And now, they have home testing machines, much like blood sugar monitors that you can do yourself. Our doctor at first did not like them because of a problem, but they later figured that out and he said they now work well.
Dale