How to remove paint from an indoor brick wall

This all depends on how long the paint has been on the house and what kind of shape it's in. Because brick is a porous material paint adheres very well to it. I think your first step would be going to the local paint store and rent a power-washer. A gas powered power-washer. You are going to need as much psi as possible (at least 3000+) with a pin-hole revolving tip. This will blast away any paint that is loose on the brick.

This should be less damaging to the brick and mortar than sand blasting.

Depending on how successful this was in removing paint dictates your next steps, if most of the paint is gone, then maybe just a wire brush and some paint remover will get the job done. If you've power-washed your whole house and it is still covered in paint, then I would call a contractor and get quotes.

This E-How article says that a soak with your normal shampoo, followed by running a fine-tooth comb through the affected area(s), should remove water-based paints including latex acrylic. By fine-tooth, I assume they mean a comb like a pocket or dressing table comb, but you may have more luck with something like a lice comb.

Now, latex paint with VOCs may cause other types of discoloration, similar to thinners (which is why you NEVER put paint thinner on your hair; no turpentine, no acetone, no methylated spirits, no nothing). Also, certain dyes, like red and orange, will soak into surfaces (even some things you wouldn't consider "porous", like ceramic tile) and become extremely difficult to remove. I dunno what color you painted the closet or exactly what type of paint you used, but it may not be a layer of actual paint causing the discoloration anymore.