"in the following days" is a grammatically correct and usable phrase in written English. Example sentence: I'm looking forward to spending time with my family in the following days.
In the following days, agents swept in and arrested them.
In the following days, his vision started to deteriorate.
In the following days, 450 readers responded to the article.
Nevertheless, more homes were destroyed in the following days.
In the following days, Latte resumed his old contacts.
In the following days, each former student spoke.
In the following days, thousands joined the protest.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com