There are a variety of problems, but some that come to mind:
1) The CSA does not have much in the way of ships and hard currency. Even without the cotton embargo, it can't afford much. And sinking that money into cotton that will sit in warehouses for later loans might not be the best investment when it needs weapons and so on now.
2) At least to Britain, the warehouses already have significant supplies of cotton. That's the real problem, not India and Egypt. Why's Britain going to worry about a cotton shortage that doesn't exist?
3) Britain has no reason to want to support the CSA. Unlike say France in the American Revolution - which saw it as some way to strike it at a rival - Britain has no stake in the US losing the war.
4)
http://www.civilwarhome.com/cottondiplomacy.htm
Almost unanimously, Southerners believed they could use cotton to lure England and France into recognizing the Confederacy.
Since the administration of Jefferson Davis wanted to avoid any appearance of international "blackmail," the Confederate Congress never formally approved an embargo, but state governments and private citizens voluntarily withheld the crop from the market in hopes of causing a "cotton famine" overseas.
Changing ol' Jeff isn't enough to change the mentality of the Confederate congress (quite willing to oppose him) or the individuals who were the ones actually executing it.