Is it normal for a puppy to follow you everywhere?

Yes, because all canines live in packs, where they have a leader, the alpha male. The puppy follows you because it recognises you as the leader of the pack, regardles your sex. Also, when they grow, they are more hungry than not, so it expects food from you (as in the pack). But, do not feed him all the time. Remember: small pups two meals, grown dogs one meal a day.