You will have to cure the shopkeeper now to continue. It is a task that everyone gets after day 14. You did not do anything wrong.
Study about his sickness in your notebook at home. You will learn the recipe for Spectral Sirup, the cure for his illness. You will also see Heat Occisia in your notebook when you have finished studying. It is an ingredient you have to craft first to be able to craft Spectral Sirup.
If you cannot figure out the recipe for Heat Occasia from the description, you can visit Othra the lizard priestess in the lizard's Ruin.
If you have not unlocked the Ruin, now is a good time. Explore the Swamp until you discover Something Interesting, you will have to make a few choices and eventually meet a lizardman who will take you to the Ruin where you can meet and talk to Othra.
Once you craft Heat Occisia then Spectral Sirup, visit the shopkeeper in the daytime and you will have the choice to give him the medicine. You will need to wait a day and return to check on him. The game will move forward after that.