The other answers correctly point out that "thalidomide" is a generic drug and is not trademarked. But I'd like to answer the more general question, which is if/how you can refer to a trademark in a work of fiction.
In a website article, Using Trademarks in Fiction, the author describes 3 issues to consider: “product disparagement,” “trademark dilution” and “trademark tarnishment.”
Product disparagement would be the main issue in your work. Technically it's only a problem if your claims are false, but we know that large companies will bring suit anyway if they feel the need. The costs for them in a garbage suit are few but they can control the press and bankrupt the writer. In the US, it doesn't matter if you're right, it matters if you can pay your lawyers.
In another web article, Can I Mention Brand Name Products in My Fiction?, the author focuses on 4 issues: "trademark infringement," "trademark dilution," "trademark tarnishment,"and "defamation."
Here, we also have recommendations of an abundance of caution. Big companies can be really touchy.
For example, the director Danny Boyle, told the press that he caused
Mercedes Benz logos to be digitally removed from cars in his film Slum
Dog Millionaire when the manufacturer objected to the depiction of its
cars in Bombay slum settings.
Makers of movies and TV shows generally are a lot more careful than book publishers, because of the wider audiences and more obvious references.
I have not found legal references for what to do when a product is widely acknowledged as having caused harm. Certainly it is okay to talk about (or even show explicitly) the dangers of cigarettes or lead. These aren't trademarks but they both have powerful lobbyists and industry groups. Remember how the beef industry went after Oprah for talking about mad cow disease on her show in 1996? She ultimately won, but only after a lot of her time and money.
So it depends. If all you're doing is mentioning that a character has a disability caused by thalidomide, even if it were a trademarked product, you're probably fine, as it is well-documented that these cases happened.