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Hello this is Dr. Holloway, but you can call me Dr. H for short. I am sorry Shadow seems to have injured himself. Do you happen to have any Epsom salt or can you purchase some at your local pharmacy?
If so I would recommend soaking the affected paw in Epsom salt for about 10 minutes to help with soreness. You can do this 2 times a day to help relieve the pain. Typically it only takes a couple of days of this and then you can discontinue because the nails can grow really fast in younger dogs.
If there is no continued bleeding you should be fine where you don't have to cauterize anything. However, placing a moderately loose bandage on the area is helpful so the pet does not re-injure the area. Placing a Tefla pad on the wounded area first, then place some cast padding on top of that , then applying some stretchy bandage material (like this one http://www.cvs.com/shop/health-medicine/first-aid/bandages/molnlycke-health-care-tubifast-2-way-stretch-tubular-bandage-2-in-x-11-yd-skuid-585592 is helpful to apply continuous pressure to the area to keep it from starting to bleed again. Just make sure you check the bandaged area every hr for the first 4 hrs to ensure it is not too tight and causing any stop in blood flow to the bottom of the paw (the paw will swell if this is the case).
Here is a link to the Tefla Pad that I was talking about. http://www.cvs.com/shop/health-medicine/first-aid/first-aid-tape-gauze-pads/telfa-ouchless-non-adherent-pads-6-x-3-in-50ct-skuid-545925
If you can't find cast padding, a couple layers of gauze may do the trick. Then you can cover the entire area. Also stockinet's can be used to cover everything and keep it in place.
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