Some of the folks responding are confusing anal fissure and anal fistula. They are two different things, treated differently.
Anal fissure is indeed a tear in the lining at the anoderm, which becomes chronically inflamed and nonhealing. There is stinging and burning with bowel movements of course (any cut would burn if you rubbed poo in it, right?).
The very severe pain that you are experiencing is something different, however. It occurs when the anal sphincter - a ring of powerful muscle - goes into a spasm. You know those leg cramps that we've all experienced at night, where you wake up and your calf or foot is locked into a cramp? It's excruciating. You jump out of bed, hop around, scream, cry, massage it, and pray for it to pass. Well, that's what is happening to your butt when you have those very severe pains. Your anal sphincter is locked into a cramp that won't break.
That's the idea behind the topical nitroglycerin, or the botox injection. It causes muscle relaxation. Once the muscle spasms stop occurring, the tear will heal. We don't know why exactly, but we know that it's true.
If conservative care fails, the surgery to treat chronic anal fissure is called a lateral internal sphincterotomy. It involves cutting the muscle part way through so that the spincter cannot lock into spasm. It works very well, but you can accomplish the same thing with a botox injection. If you see a colorectal surgeon s/he will be well versed on all of the options to treat chronic anal fissure.
Good luck.