There are several things that can cause a dog to drag their rear on the floor. This can be due to anal gland problems, tapeworms or allergies.
If your dog is dragging their behind on the ground or carpet and their anus area has a bad odor and swollen, it can be symptoms of an anal gland problem. This is probably the problem since your dog's anus is swollen. This may cause a dog to continue to lick the area.
The anal glands are 2 sacs on either side of the anus at about the 4' o'clock and 8 o'clock positions. If your dog is continually licking their anus and dragging it, it could also indicate that they are full. This problem can usually be resolved by emptying out the glands. To empty them or express them, you will want to cover the area with a tissue and press your finger on the dog's anal glands with an upward motion. A foul smelling liquid should come out. If nothing comes out and your dog appears to be in pain, then your vet will probably have to do this. Your vet can do this easily, as he is experienced at it.
Excellent site on anal glands
If no lump in area It could also be tapeworm infestation. Tapeworms release segments that exit the anus and spread tapeworm eggs into the environment. They can cause severe itching in some dogs. They can usually be seen in the stool and are small about 1/2 inch moving things. If the stool has dried, they look like rice in the stool or stuck in the hair around the anus.
The last is allergic condition -- flea allergy being the most common allergy leading to itching around the base of the tail and rectal region.
You can put rinse the area well and apply some hydrogen peroxide and tripple antibiotic cream or neosporin on the area which may help a bit if you can not express the anal glands. In addition, most groomers can also express anal glands as well, if that is the problem. With bleeding though, the anal glands may be infected, unless the bleeding is from rubbing his rear on the carpet.
I hope you find this information helpful.