This is a complicated one: US generics are vastly more expensive than international generics, but at least part of that is because US manufacturers sell those drugs abroad at the cost of production, making up their remaining costs in the US. People in the industry have described it to me as a tactic of "we help people in need, please don't regulate us".
This isn't the whole story; east Asian manufacturers also produce cheaper products, for a bunch of reasons from lower costs to lower regulation to lower profits. And it's notably not the case for non-essential, non-basic medicines (e.g. most psychiatric meds), expensive new generics not used abroad, and certain other high-demand generics like insulin. Those are either expensive everywhere, or more expensive in the US than other wealthy countries and largely unused in poorer countries. (How all this relates to your story depends a lot on whether we're talking about Bangladesh or Taiwan.)
But as far as generic antibiotics or antihistamines, it's going to be hard to separate "US manufacturers overcharge" from "US manufacturers sell cheap abroad".
I should have been clearer about "abroad"; I didn't mean Europe. Trump is referencing the claim that Americans pay for drug development and Europe gets cheap products from it, which is dubious at best. And I don't think US-developed medicines are being sold at-cost there, even if they are cheaper.
What I'm talking about is medicines that are donated, sold with differential pricing, or assigned 'voluntary licenses' to increase medical access in underdeveloped countries. Voluntary license medicines are required to be produced with substantially different appearances from their developed-nation analogues, specifically so that they won't be exported back to undercut those products.
All of those programs are fundamentally good things which save lives, but they lead to some pretty strange outcomes and in turn strange reporting. It can be vastly cheaper to obtain a medicine in an underdeveloped country with supply shortages than in the first world, and that sometimes also prompts articles saying that such-and-such a medicine "only costs 10 cents in other countries!" As far as I know, this is mostly an issue in the US; most other high-differential-price countries have socialized healthcare or other functional solutions like Singapore's, but the US has a lot of extremely poor people who end up paying much higher prices than equally impoverished people abroad.
This isn't the whole story; east Asian manufacturers also produce cheaper products, for a bunch of reasons from lower costs to lower regulation to lower profits. And it's notably not the case for non-essential, non-basic medicines (e.g. most psychiatric meds), expensive new generics not used abroad, and certain other high-demand generics like insulin. Those are either expensive everywhere, or more expensive in the US than other wealthy countries and largely unused in poorer countries. (How all this relates to your story depends a lot on whether we're talking about Bangladesh or Taiwan.)
But as far as generic antibiotics or antihistamines, it's going to be hard to separate "US manufacturers overcharge" from "US manufacturers sell cheap abroad".