I have to assume you have a color of paint currently coating your brick and wish to change it?
Under that premise I have to start by informing you of the possibility of lead contained in the paint, especially any home prior to 1978. Renovation, repair and painting (RRP) projects are typically performed at the option of the property owner for aesthetic or other reasons, or as an interim control to minimize lead issues. It is not designed to permanently address lead-based paint. However, RRP projects can disturb lead-based paint in homes and buildings built before 1978 and cause lead hazards, even when none existed before. Therefore, they are also regulated and require certification. If you would like information on EPA's rules requiring lead-safe renovation, repair and painting to prevent lead hazards see EPA's Renovation, Repair and Painting (RRP) Program page here.
Sandblasting describes the act of propelling very fine bits of material at high-velocity to clean or etch a surface. Sand used to be the most commonly used material, but since the lung disease silicosis is caused by extended inhalation of the dust created by sand, other materials are now used in its place. The negatives of sandblasting are the noise, dust, mess and containment. During the process it is often difficult to see the surface as the dust cloud is prevelant. You often have to work an area, wait for the dust to settle, review your work, then continue.
However, there is an alternative type of blasting that reduces dust, particle rebound and waste. There is a company called Sponge-Jet that has abrasive medias mixed with sponge. By using Sponge-Jet you reduce the bounce off by typical sandblasting thereby reducing dust by 90%. Since there is limited rebound you can actually see the work progress so you don't have to stop. The residue is easy to clean up and remove because you don't have the blow back. Since you can use varied degrees of grit you can use it for the most delicate smoke removal and historic restoration to industrial bridge repair. And the best thing about Sponge-Jet is it is reusable. I have seen this product used on brick, stone, wood, steel and concrete. It was used to restore the Wisconsin State Capital. It is enviromentally safer than regular sandblasting because you can easily control the media containment for disposal and or filtering.