When I was a kid, I and others did use Sloan's Liniment for a sore pitching arm, or a twisted ankle, or other hurt muscle. I suppose all it did was provide a counter-irritation so bad that you didn't mind the original hurt. Capsicum pepper grease did the same thing.
Rubbing Vicks Vaporub on your chest and applying a warm, comforting neck cloth eased the breathing of a child with pneumonia. If things were really bad, one obtained a wicked-looking Vapo-Cresoline Lamp that provided a smelly vapor to open up one's airways. It was used to save my life when as an infant I nearly died of croup.
For chapped hands, one used Corn Husker's Lotion ; and kids sold Cloverine Salve from door to door (both still available). It was said to be good for warts, moles, sore holes, and pimples on the nipples. But the truly very best healing salve for cuts, light wounds, abrasions, or anything that could get chapped and infected was Bag Balm, a black, stiff salve in a square can. It was always in every cow barn, and its uses are many, for example "squeaky bed springs, psoriasis, dry facial skin, cracked fingers, burns, zits, diaper rash, saddle sores, sunburn, pruned trees, rifles, shell casings, bed sores and radiation burns." Bag Balm is also still available. (I could have sworn that before antibiotics, in the 1940s and before, the can contained teat wicks immersed in the salve, and used for treating mastitis, and what you used was just that left over after removal of wicks. But I could be quite wrong--an old dairy-farmer could tell you.)
Band-Aids were for the upper class wussies, who could afford such treatment for their little "boo-boos." A real cut demanded a cut or torn inch-wide strip of clean, worn-out old linen wound about the cut. The end of the strip was slit back a couple or three inches to provide a method to tie the wrapping in place. Then on with finishing the work one had to do for the day.
Of course, every one knew that aspirin was a refinement of the acetylsalicilic acid leached from chewing bark stripped from a willow branch --
I lived across the road from you. Remember the skinny blond kid who always hung around with the older boys? That was me.