Hi, Tammy. There is only one, or possibly two, good answers here. The first is to remove and replace the brick on the fireplace. The second is to remove and replace your new tile floor. When you went to the tile store, you saw samples of what your new floor would look like, right. Did the fireplace suddenly appear since then?
Some people believe that you can just paint the brick. This is a bad practice for your safety, your cleanliness and the brick. By painting the brick, you are taking a surface that is totally fireproof and making it capable of giving off fumes, if not worse, in the event of a fire in your house. As you will see from looking down this board and others, removing paint from brick is a major headache and it is probably easier and safer to replace the brick than strip it. It is more expensive also.
At best, it is much harder to clean painted brick than natural brick. The problem with this is that you increase the possibilities noted above.
Lastly, brick is a product that is meant to breathe. It probably will not mean a thing in your time in the house, but 50 years or so from now the 14 coats of paint that have added up over the years will compromise the brick and it will have to be replaced anyway. Who knows what will happen in 50 years, but I'll bet that it will be proportionate a lot more expensive than it is now.
I suppose that you could build a box around the fireplace with appropriate fireproof materials. You would have to be very sure of meeting local and national codes should you attempt this. If you try to do it without meeting the codes, your fire insurance policy may not cover you even if the fire had nothing to do with the fireplace.
You might think that I am being real mean and nasty about this and I am. But I see this question so many times and in so many variations that I do want to stress thinking ahead and doing your homework in remodeling projects. It is a lot easier and cheaper to do it right the first time. But don't feel too bad, the local paint store will not let me choose anything to do with the color of paint without a note from my wife, and I have "been there, done that" often enough that I agree with them completely. I don't want the grief either when my wife and daughters don't like the colors I choose.