Not necessarily since the U.S. was not the only, or even the largest consumer of the output of the UK textile industry. They also enjoyed the advantage of being the closest and largest supplier of raw cotton. Demand for their produce was high and as a result the U.S. tariff couldn't have had much effect on their exports, if it had any effect at all.
U.S. tariffs on finished imported goods, beginning in 1816, were designed to protect emerging manufacturing firms, located principally in the Northeast, from foreign (primarily English) competition. As these tariffs especially affected (indirectly, as explained previously) the market for raw cotton, South Carolina politicians fought these tariffs relentlessly, leading to the so-called nullification crisis of 1832. Henry Clay, aka The Great Compromiser, led the way to passage of legislation in 1833 which specified the gradual lowering of tariffs to the level existing in 1816.
The tariffs were a huge deal to politicians in both the North and the South, and almost led to South Carolina’s secession in 1832. They must have had, or at the time were perceived to have had, large effects and gave rise to the first militarily relevant sectional conflicts in the U.S.