“... you could sew your own shirts, bedsheets, and other products.”
Of course, this is still true today but few people do so because it is much cheaper to buy manufactured finished goods. This was also true in the 1820’s, but this fact does not refute the argument that high tariffs on imported finished cotton goods reduced the demand for raw cotton harvested in the South. Moreover, the argument that the tariff was not important to Southerners (especially South Carolinians) is counter to the decades-long campaign they waged against it. The tariff of 1816 was 20%, not .5%.
So if the textile mills in the North which used 100% Southern cotton were forced out of business by cheeper imports from England and France who used maybe 90% Southern cotton, demand for Souther cotton would be higher?
That makes no sense at all which is likely why no one made that argument in 1860.
No, your argument has a flaw. There was a study of this in the Journal of Economic History. I think the authors are C. Knick Harley and Peter Temin. Basically they found that the tariff did NOT hurt Americans, that the imports we had (esp. in the south) were different types of finished textiles than the U.S. produced. In other words, we would have bought them whether the tariff was there or not at the same prices. The more work that economic historians do on the tariff issue, the weaker and weaker it becomes as an issue for secession. The data is not on your side.