I am spending my experience points from the BC on my pet Alex the Great Dragon to raise his health the points are disappearing but my health is not going up .... is there a delay when using my experience points

Using your EXP will increase your pet's stats right away, however there is a 5 minute (I think) cache on the Your Pets page. So you won't see the numbers on that page update right away. What I've been doing is going to the training center and refreshing there when I spend my EXP, because that page updates the info right away so you can see how much you're increasing each stat.