There were plenty of American exports of the time besides cotton and tobacco. Whale oil out of Nantucket and metal from Northern mines, for example. Also, Great Britain, where the great textile mill industry was at the time, had an interest in fostering cotton imports from her own colonial areas, like Egypt and India. You could as well say the tariffs aided American industry at the expense of Great Britain's.
The real question is why the South never tried to develop their own domestic textile industry. Or any other significant manufacturing, for that matter. One of the main reasons the South lost was the inability to manufacture the goods needed in the face of the blockade.