You don't determine the tax to which you might be subject on the off chance that you, acting through a UK Limited Company (your question says "if I sell" but later explain it is an organization making the deal and not you after all), sell a T-shirt to a US individual. In short, this transaction could be subject to both pay and deals tax. I'm excluding customs duty since that will be forced on the buyer upon import into the US.
Without more facts, it is difficult to offer a definitive response, but for reasons for this question, I will expect you are selling from a UK website or otherwise absurd without a third-party intermediary.
To the extent annual tax goes, given that title to the T-shirt passes in the UK, there ought to be no US government personal tax because the UK organization has no presence in the US and the offer of tangible individual property is sourced outside the US if the deal doesn't take place in the US. You could likewise guarantee the benefits of the annual tax treaty between the US and the UK and given that the UK limited organization doesn't have a "permanent establishment" (office or other fixed business environments) to which the offer of the T-shirt could be attributed and it meets at least one criteria in the limitation on benefits article.
