This is the closest short story I could find about a mouse and aspirin: The Mouse and the Motorcycle by Beverly Cleary It was wrote about the right time (first published in 1965) however the story differs from your memory. You can read a good description of the book by clicking on the link below.
It's not really a short story, but perhaps it was Mrs. Frisby and the Rats of NIMH. Mrs. Frisby is a mouse who is trying to find medicine for her son.
I was a huge Beverly Cleary fan when I was in high school. From the details you've provided, I would have to say I think you're talking about "The Mouse and the Motorcycle. " Ralph S.
Mouse does go in search of aspirin, but it's for the young boy who owns him. It's not technically listed as a short story. It's a fiction novel for young kids, so it is fairly short (176 pages with large print).
To see if this book matches the story you remember, you can preview it on Google Books - books.google.com/books?id=020vfe93e3YC&p....
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.