I've begun potty training my 3 year old daughter, but she fearful & is holding it for a long time (one day for 18 hours). What can I do to help her?

Several things. First, the ability to be toilet trained depends on neurological maturation. Second, toilet training is a skill that is easily shaped through positive reinforcement. Failures should be ignored and successes praised. Putting too much emphasis on the toilet training and failures can increase the child's resistance. Most children learn this skill easily if done in a relaxed manner.