Yes, atmospheric pressure is primarily caused by the weight of the atmosphere above you. This is why the pressure decreases as your altitude increases.
A fluid (like air) under pressure exerts equal force in all directions while at rest. [Side note: Technically it exerts slightly more force downwards because of gravity. However, this effect is only noticeable on scales much larger than what we are dealing with here, so I ignore this effect in this answer.] So the air at ground level pushes equally on the ground beneath it and the air next to and above it. This is the pressure that you constantly feel. Now imagine yourself in a gazebo - a roof above you, but with open sides. Clearly, the air pushes on you from the sides. But the air above you is also pushing down on you with the same force per area. Why? The air above you is being pushed on the sides, which means it is under the same pressure that you are. It pushes back against the air compressing it from the sides and pushes in the vertical direction, both up, against the roof of the gazebo, and down, against you.
While rooms have walls, they are not airtight, which means that air can flow through them. If the pressure inside the room is different from the pressure outside, air will flow to "balance out" the pressure imbalance. In effect, any room is like a gazebo - the pressure will remain basically the same inside and out if nature/physics/entropy is allowed to run its course.
That being said, if you are willing to do some work, you can change the pressure inside a room - see