Lisa, just a guess, but this does sound like a product called Z-Brick. This comes in pieces that looks like a few "bricks" put together--usually 4 bricks. If you can see lines where the 4 brick panels are put together, this is probably what you have.
As I'm sure most of the old timers here know, I hate painted brick. But since this is not brick, go ahead. I would suggest that you go to a specialty paint store, not a home center. Tell them what you have and you night take a digital picture or 2, if you can. They will suggest a primer and a paint. The kind will depend on how you want it to look and they will insure that the paint and primer are compatable.
If you do decide to get rid of Z-Brick some day, it can be done fairly easily. It is usually held on with glue and removal will probably tear up your drywall that it will be easier to replace the drywall than to patch the bad spots. This isn't hard or expensive.