Since I do not know your health history or the reason you should avoid anti-inflammatories I cannot answer this question. Please consult with your Dr. or send us more details.
For those taking Coumadin it is important to keep a consistent intake of Vitamin K so that your Dr. can adjust the dosage of your medication. It isn't necessary to avoid vitamin K containing foods completely, but more so to make sure you eat the same amount daily.
Here's a list of vitamin K content of various foods:
Please discuss with your Dr.