On my phone when charging a small lightning bolt appears on the battery symbol to signify charging also a tiny led lights up orange and turns to green when the battery is fully charged.
There are a couple of options that you can do if you chose to.
1. It's possible that the red x should not be there and you should get a different one and the red x is a way for the phone to tell you that there is something wrong with the battery , even though it's charging. Have you looked at the owners manual for the phone ? It will tell you the process of the battery charging and it will tell you what the screen should look like and if the symbol should be a red x or something else.
2. Buy a new battery and see if it does the same thing , I know that's costing money but if both are good then you have a spare battery and if not then you have your solution if the new battery gets rid of the red x.
3.If you don't want to buy a new battery then try going to the cell store and asking them , they can tell you right away if it should be there or not.