Well, English prefers to be more specific. The Russian sentence essentially means that whoever is going to do the action in question (or take part in certain activity) is going to have their arm sore. In English one would likely say such a sentence using a generic "you" (your). Or, indeed, "I" (my) if the sentence is about yourself.
For me (UK native speaker), "sore" is a very specific kind of pain. To say something will hurt is very general (the type of pain might be a sting, an ache, whatever). To say it will be sore suggests a particular kind of pain - probably with a sensation of heat, and there might be inflammation.