Hi!,
I'm also a singer. I don't sing in a band that performs many times a week, but I do sing in a band for the church I am music director at. I practice daily for about 1/2 hour. I have a 3 hour rehearsal one day a week and sing, for almost 2 hours on Sunday. I've done this for 11 years, have been on Coumadin for 13 years. I agree with Ross, I think the No Singing Full Out With Coumadin is an urban legend. Believe me, I can sing full out.
My guess is that there are many contributors to your problem. If you've stepped up singing time and rehearsal, you probably already have been putting a strain on your vocal chords. The cold came along and made it worse. If you were taking decongestants, that probably dried out your chords more. Not working gradually back into your voice after a cold can wreck havoc on your chords. If these things caused irritation, then (just like nose bleeds) you will have a greater chance of bleeding because of the Coumadin, but the main damage was most likely there due to the cold and other factors and the bleeding was a byproduct.
I'm sure your doctor has given you directions on how to proceed. Drink lots of water, work back into your voice slowly once you have been told you can sing again (don't know if he told you to lay off). Make sure you work on getting rid of the tension points (jaw, neck, forehead, shoulder tensions etc. all put strain on the chords) while singing.
I really try to nip any cold in the bud before it takes route. I take a really good multivitamin and haven't had a major cold in several years. I had them all the time before I started vitamins. If I feel a cold coming on it's Zicam to the rescue.
Best wishes in getting your pipes back.