Ok, an antibiotic won't hurt it, BUt, you mention it is raspy AFTER you bottle feed it......this is common, as it usually means that a small amount of milk has been aspirated into the lungs..............not good, but often does not cause any long term harm.
As for giving antibiotics to everything that enters the farm, I would frown on that
, if anything, isolate it and make sure that it has all of it's AGE APPROPRIATE vaccinations, colostrum if still within the 12-24 hour birth window, and use antibiotics only when needed.
When it comes to bottle feeding calves, cleanlyness is the key here. Prevent cross contamination.......just consider everything you touch, and everything a calf touches, healthy looking or not, as being potentially contaminated, and don't pass it on to others or you for that matter..
My hands stay somewhat dried out due to all the washing and bleach we use around here.
JMHO :cboy: