Ask yourself why you would find brick or ship lap on the interior of your house.

You answer will tell you where it might go.

In the houses I've lived in with interior brick, it was always on a wall that was originally outside, and the space was enclosed and over time incorporated into the house (windows, insulation, heat and ac). Oh, and a grill, warming drawers, oven space in the kitchen; made sense since the grill had a chimney.

But it only belongs on a wall that might have been an exterior wall. So in the above picture, it might not suit.

bpath is correct that you will sometimes find brick on the interior of a house if an addition was made and the original brick exterior was left exposed. But there is another condition where you would find brick naturally exposed in the exterior walls of houses: many brick houses built before 1940 and virtually all brick houses built before 1900 were built with load bearing solid masonry walls that were anywhere from 2-4 bricks deep. For instance if we tore off the plaster in our 1920s house, right behind would be brick. The brick on the inside surface would be common brick, not high quality face brick and the color would vary per region. For instance in the Chicago area, common brick is a yellow buff color. In other places it may be soft and orange red. So you could do brick on an exterior wall with flush mortar joints and maybe even give it a lime wash to suggest that it had been covered up and recently rediscovered. This particular look would suggest a home that has age and history. Think of the story that you want to tell.

As far as doing brick and ship lap, any one space should have only one accent wall, or at most two accent walls that are both treated the same. If you start doing every wall in a different material, they start competing for attention and you loose a sense of cohesion. I would instead consider either 1.) Doing either brick or ship lap and keeping everything else drywall 2.) Picking either the ship lap or the brick to be the focal point and doing everything else in the other material or 3.) use the ship lap either as a wood ceiling feature or as a wainscoting that goes up only 30"-4' on all walls so it becomes a unifying feature rather than another focal point.

What does your architect or interior designer recommend?

When brick is treated like paint it usually does not turn out well.