When Junior had his nosebleeding my vet put him on Vitamin K. I think it did help. He didn't have as much bleeding as others on this thread. It was an easy pill for him to take. I am also a nurse and we use it alot at the hospital to treat people for bleeding disorders, it works well.
Although Junior didn't have as much bleeding he still had the horrible sneezing attacks and swelling that pushed his eye up, we didn't use any steroids but the vet did offer them. I hope this helps, good luck.