Audrey - The mixing valves, cartridges and "innards" of your shower may been worn and in need of replacement. The greatest concern when you see the constant drip is what is happening behind the wall. Often when the drip continues into the tub, the plumbing behind the wall is an issue as well - thus it is better to be safe than sorry (especially if the shower is above furnished space) and call in a professional.
If you do tackle the repair on your own, make sure you know where the water shut-off is prior to doing the work. Match up the shower type with Eljer's product list. Their website, linked below, provides the specific parts per each product.