Upvote:1
Standard answer:
If you booked this on a single ticket (for example United to Lufthansa), the luggage will get checked through to the final destination. You MAY be able to take an airside shuttle from C to B and not have to go through security again. See https://www.newarkairport.com/at-airport/connecting-flights. 3 hours should be plenty
If you booked this as two different tickets, you need to exit the secure area, collect your bags, bring them to the check in counter of the departing airline, and go through security again. 3 hours may or may not be enough for this and you carry the full risk of a missed connection.