I've been using warfarin for 25 years and don't recall nosebleeds. If you've got a meter, it probably wouldn't hurt to check your INR to confirm that it's in range when these (at least one or two) nosebleeds occur.
The sinus rinse mentioned by **** is probably the one from NeilMed. It's available at RiteAid. If you belong to Costco, they've got the best deal for these - two (or three?) bottles, 250 packets of the sodium chloride/sodium bicarbonate power that is used to mix the rinse solution, and a can of spray to moisten your sinuses. If you don't belong to Costco, I found that the packets are less expensive at Target than they are at Rite Aid.
I've stopped using the sinus rinse - not because it didn't help, but because I'm basically a bit lazy about self-care, and it's a bit weird putting the bottle in a nostril and squeezing the bottle so that the solution comes out the OTHER nostril.
I may wind up going back to it when I think that I REALLY need it.
I wish you a quick resolution to your nose bleed situation.