Aw no (
I have my first ever ill villager in New leaf, after having my original town for 5 weeks, and my new one for nearly a month, and its Stitches bless him
how long does it take them to recover?? ive just given him medicine
A few days as everyone here has already stated! Give them medicine everyday (or at least once) and they'll write you a little letter and maybe post a little present for you for being so caring. (At least Nibbles did that in my old town!)