These words have overlap in meaning but they can be different in usage and it would sound weird if you use them interchangeably.
爱惜 means to love something very much and want to protect it;
爱护 can mean you love someone or something alive like flowers, animals, and worry about what happens to them so you have the need to take care of them.
珍惜 is often used in something abstract like relationships, your wealth, health etc
Hope this helps