Lisa, is this on an outside wall or an inside wall? Why would a brick wall be there? How old is the house? If it's a really old house, was the brick part of a chimney? Is it still? Sometimes "removators" from years ago left chimneys in place, rather than tear them out, when doing a rehab or addition. If that's all it is--and you are sure that it's strictly decorational now--the choice to paint the brick is yours. But once you paint, you will not have an easy option of anything other than paint in the future.
If it is part of an outside wall, why not build a framed wall in front of it? Insulation? These are the kind of questions that come up when I can't see it. Sorry if they seem dumb, but I really don't know your situation EXACTLY.
I just bought a white Melamine base cabinet for $75. It found me. I wasn't looking for it. But that's about half the retail price. You might try cabinet shops and the like to see if they have anything that was mis-ordered that they want to get rid of.
I really would not suggest painting either your brick or your cabinets. You may want to change them one day. Stripping brick is difficult to impossible to do right. If it's on an outside wall, it can change the humidity level in your house and cause or cure a lot of problems but I would not be able to say which without seeing the whole picture.
How about the other walls? Can you paint those? Do you have any furniture or built in things like a breakfast nook?
Lisa, I don't want to cause you future problems either, so do go slowly and be sure you are right before you act.