Hip surgery is a major undertaking and swelling to the limb on the side of the surgery is quite common. While I agree a Coumadin allergy could be the cause, it is not a common thing to see. Much more likely as a cause is the swelling (venous insufficiency) in that limb. Also keep in mind that infection in the limb is always a concern after a joint surgery and should be considered when you see a rash. Swelling itself can be improved with elevation and compression hose along with ambulation as recommended by the doctor in charge of his case.
To best tell what is going on will require a doctor's visual and touch exam.
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