Let's start with the good news - there are no eggs or egg products in shortening. So we can dispense with that part of your question.

Traditionally, the word shortening referred to any solid fat, including butter, lard, and suet - some or all of which are not appropriate for you. But nowadays, when you see the word shortening in a recipe, it is referring to a solid fat made from vegetable oil. Hydrogenating the oil, that is, adding hydrogen gas to it at a high temperature and pressure, is what transforms it from a liquid at room temperature to a solid. Vegetable shortening is flavorless.

We're not sure where shortening turns up in a tortilla recipe - traditionally it is made of corn flour and water, and cooked on an ungreased griddle. If your recipe calls for shortening to grease the griddle, of course you can use any fat you like, or you can be resolutely traditional and omit the fat. If it is an unexpected ingredient in the tortilla, vegetable oil, butter, or margarine would serve as a substitute.