HI AMBERLISE ~ sorry to hear of your situation; I was in a similar one some time ago and was also on Coumadin for a year for a clot in my leg (caused by a fracture). I did some research at the time; and found out that indeed, it is believed that some kinds of foods thicken the blood (esp those with Vit K in them, like dark green veggies).
I thought the light green ones were OK; correct me if I am remembering the info wrong. I thought that ICEBERG head lettuce and Celery were OK; but, check on that first ... thru your doctor ...
Watch your sugar intake as well, and limit the tomatoes to a few times a week; my sources said that *excess* amounts of sugar can thicken the blood also. A good tip would be to scan the veggie & fruit section for anything that is red, yellow, orange, purple, blue, or white.
There are other veggies you can have like yellow beans, a small amount of corn, cucumbers (remove skin), sweet potatoes, squash and zucchini (remove skin), onions, mushrooms, carrots in moderation like the toms, parsnips, turnips (the summer ones are similar to potatoes but without the starch; so great), red cabbage may be OK, but check; beets, red & yellow sweet peppers, radishes, potatoes, and eggplant; plus all fruits, in moderation ~ 1/2 cup.
Radishes and cucumber (w/o skin) make a nice sandwich with salmon and/or light cream cheese.
What is Jicama; never heard of it and would like to know. I hope these suggestions are helpful. Becuz of the seriousness of your condition, please run these ideas by your doctor first, OK?
ROSEBUD