Welcome to HCM,
Your daughter is taking oral anticoagulant warfarin
which is prescribed for clots in lungs in her case, we need to monitor effect trough PT (INR) which should be between 2-3 .
If INR is not in desirable range then dose of warfarin is increased and with caution that if INR goes too high there may be bleeding.
To have effect of warfarin you should take care of diet avoiding green vegetables and cruciferous in diet which are rich source of Vitamin K1.
It is good that there are no clots in scan,you should just take medicine regularly and monitor with INR.
Please do not worry about increasing dose of warfarin it is just to reach to desirable level of anticoagulation.